
Class T^fi- jS^ 
Ronk -U (o 



/f/^ 



DEPARTMENT OF COMMERCE 

U. S. COAST AND GEODETIC SURVEY 

K. LESTER JO^sTKS 
SUPERINTENDENT 



SURVEYING 



A PLAN^E TABLE MANUAL 



BY 

X). B. A\rA.I]SrV/RIGHIT 

-A-ssistant 



APPENDIX No. 7-REPORT FOR 1905 

(Reprint, 1916) , 




WASHINGTON 

GOVERNMENT PRINTING OPPIOE 

1916 



DEPARTMENT OF COMMERCE 

U. S. COAST AND GEODETIC SURVEY 

E. IjKSTHIE, JOISTKS 

SUPERINTENDENT 




SURVEYING 



A PLANE TABLE MANUAL 



BY 

r). B. W.A.Ilsr^VRIGHIT 

.A.ssistaxLt 



APPENDIX No. 7— REPORT FOR 1905 
(Reprint, 1916) 




WASHINGTON 

GOVERNMENT PRINTING OPriOE 

1916 






ADDITIONAL COPIES 

or THIS PUBLICATION MAY BE PKOCUEED FKOM 

THE StJPERINTENDENT OF DOCUMENTS 

GOVERNMENT PRINTING OFFICE 

WASHINGTON, D. C. 

AT 

50 CENTS PER COPY 

V 



D. of D. 
SEP 7 1916 




CONTENTS. 



PRELIMINARY- STATEMENT. 

Definitions: Page. 

Topographic map 295 

Projection 295 

Scale 295 

Datum plane 295 

Relief 295 

Control 295 

INSTRUMENTS. 

Plane table • 296 

Description 296 

The board 296 

Movements 296 

Tripod 297 

Mountain plane table 297 

The alidade 297 

Description 297 

Declinatoire 298 

Metal clamps 298 

Adjustments 298 

Fiducial edge of rule 298 

I,evels attached to rule 298 

Parallax 299 

Axis of revolution 299 

Vertical line of diaphragm 299 

Middle horizontal line of diaphragm 299 

Stadia rod 300 

Description 300 

Graduation 300 

Inclined sights 301 

Micrometer eyepiece 301 

Plane-table sheet 302 

Scale 302 

Projections 303 

Selecting limits 303 

Polyconic projection 304 

Method of constructing 304 

Rectangular 305 

Accessories 305 

Weights 306 

291 



292 CONTENTS. 

FIELD WORK. 

Page. 

Organization of party 306 

Preliminary reconnaissance 307 

Signal poles 307 

Graphic triangulation 307 

Amount of control 309 

Three-point problem 310 

Lehman's method .' 311 

Rule I 311 

Rules 2 and 3 • 311 

Procedure 311 

Examples 312 

Repetition 312 

Orienting by estimation 313 

Bessel's method by inscribed quadrilateral 313 

Tracing cloth protractor 314 

Two-point problem , 314 

Deflection of long lines 315 

Distortion errors 316 

Position by compromise 317 

Application 317 

Height of instrument 31S 

Relief 318 

Hill shading 318 

Contours 318 

Profile 319 

Advantages and disadvantages of contours and hill shading 319 

Contour interval 319 

Datum plane 320 

Reference signal 320 

Station routine 321 

Number of elevations to be determined 321 

Contour sketching 321 

Typical contour groups 321 

Order of development of contours 322 

Filling in 322 

Traverse lines 322 

Determinations for hydrography 323 

High-water and storm-water line 324 

Determination of inaccessible points 324 

Large scale surveys 324 

Rapid surveys 325 

Military reconnaissance with plane table 325 

With compass and notebook 326 

Photogrammetry /. 326 

Survey in advance of triangulation 327 

Office work 328 

Tables and formulae 330 



ILLUSTRATIONS. 



Page. 

1. Plane table and alidade 296 

2 . Plane table movement 296 

3. Alidade 297 

4. Stadia rods 300 

5. Diagram, Construction of projection 304 

6. Graphic triangulation ' 307 

7. Three-point problem 310 

8. Three-point and two-point problems 312 

9. Bessels's solution of three-point problem 313 

10. Diagram illustrating effect of distortion of plane table sheets 316 

1 1 . Hypsograph 318 

12. Hypsograph, section and views 318 

13. Diagram, Construction of profile from plan 319 

14. Crest, face, and talus of a granite cliff 319 

15. Elevation of a granite cliff ■. .1 3 19 

16. Typical contour groups 321 

17. Conventional signs 342 

18. Conventional signs 342 

19. Conventional signs 342 

20. Conventional signs 342 

2 1 . Conventional signs 342 

22 . Conventional signs , 342 

23. Conventional signs 342 

24. Conventional signs 342 

25. Conventional signs 342 

26. Conventional signs 342 

27. Conventional signs 342 

28. Conventional signs 342 

29. Specimens of lettering 342 

30. Sparsely settled town, salt marsh, pine woods, etc 342 

31. Railroads, canals, iron bridges, etc 342 

32 .■ Eroded drift banks, with bowlders set free 342 

33. Blocking of cities, etc 342 

34. Erosion of soft stratified rock 342 

35. Scale of hill curves 342 

36. Scale of shade ■ 342 

37. Diagram for reading elevations 342 

293 



APPENDIX 7. 



A PLANK XABLE NIANUAL. 



By D. B. WainwrighT, Assistant. 



Preliminary Statement.* 

A topographic map is the delineation upon a plane surface, by means of conven- 
tional signs, of the natural and artificial features of a locality. 

Every point of the drawing corresponds to some geographic position, according 
to some method adopted for representing the surface of the spheroid on a plane, which 
is called the. projection. 

Since it is a representation in miniature, the distance between any two points on 
the map is a certain definite fraction of the distance between the same points in nature. 
This ratio is called the scale. 

Each point, besides being projected on a horizontal plane, has its elevation rela- 
tive to a level surface, in some way indicated. The level surface adopted for the map 
is called the datum plane, and the representation of the variations in the vertical ele- 
ment, the modeling of the country, is called the relief. 

CONTROL. 

All topographic surveys of importance are based upon a system of triangulation. 

A sufficient number of points, whose geographical positions have been determined 
by triangulation, properly distributed over the area to be surveyed, forms the frame- 
work for controlling the accurate location of the various details. 



* Advantage has been taken of the opportunity afforded by the preparation of a new edition of 
the Plane Table Manual to make a new arrangement of the "Three-point problem," with the intention 
of simplifying the description of the conditions found in practice and the several steps required for 
the graphic solution of the problem with the plane table according to Lehman's method. This 
method is the most rapid one, in the hands of an experienced topographer, but for those who may 
have only occasional use for a graphic solution Bessels's method or the tracing paper protractor 
method is recommended. 

295 



296 COAST AND GEODETIC SURVEY REPORT, 1905. 

Instruments and Adjustments, 
the plane table. 

The principal instrument in use by the Coast and Geodetic Survey for mapping 
details is the plane table. For this purpose it is a universal instrument. All the neces- 
sary operations for producing a map are executed with it in the field directly from the 
country as a model. 

Other instruments are employed as auxiliaries to it under certain conditions, as will 
be seen later on under the head of " Field practice," but in general it fulfills all require- 
ments alone. 

Description (Illustration i). — The plane table is composed of a well-seasoned draw- 
ing board* about 30 inches in length, 24 inches in width, and three-quarters of an inch 
thick, with beveled or rounded edges. It is commonly made of several pieces of white 
pine, tongued and grooved together, with the grain running in different directions to pre- 
vent warping. It is supported upon three strong brass arms, to which it is attached by 
screws passing through them and entering the underside of the board, the three holes 
for the reception of the screws being guarded by brass bushings and situated equidistant 
from each other and from the center of the table. By means of these screws the board 
can be removed at will. 

The movements (Illustrations i and 2) of the tables in use by the Coast and 
Geodetic Survey are made from several different models, but as the principal features are 
the same in all designs the description of one type will suffice for all. 

The arms to which the board is fastened rest upon the sloping upper face of a 
rather flat hollow cone of brass, to which they are permanently fixed. Upon its lower 
edge or periphery this cone is fashioned into a horizontally projecting rim, the inferior 
face of which is as nearly as possible a perfect plane, and this in its turn rests upon a 
corresponding rim of somewhat greater diameter projecting slightly beyond it. This 
second rim forms the upper and outer flange of a circular metal disk in the form of a 
very shallow cylinder. The inferior face or plane of the upper flange or rim has, at its 
contact with the superior face of the lower, a horizontal rotary movement about a 
common center which is also the center of the instrument, and the two are held 
together by means of a solid conical axis of brass extending upward from the center of 
the inner face of the lower disk. A socket of similar shape fits exactly over this axis, 
projecting downward from the inner side of the apex of the conical or upper disk. The 
two plates are held together by means of a screw with a milled head, capping the cone 
from the outside, and which can be loosened or removed at pleasure. 

A tangent screw and clamp fastened to the edge of the upper rim permit, when 
loose, the revolution of the table about its center, and, when clamped to the lower limb, 
hold the table firm while the tangent screw gives a more delicate movement. 

Three equidistant vertical projections of brass, grooved on the underside, and cast 
in one piece with the under face of the lower disk, extending from the periphery toward 
the center, rest upon the points of three large screws which come through a heavy 
wooden block below. This block, which is the top of the stand and is approximate in 
form to an equilateral triangle, is 23^ inches thick when made of wood. 

* It is contemplated having the board made of a special aluminum alloy. 




1*T 




1 ' ^^- 


'i '■ 




j r 








tr 




w 






PLANE TABLE MOVEMENT. 



APPENDIX 7. A PLANE TABLE MANUAL. 297 

The three screws last mentioned have large milled heads, are quite stout, and play- 
through the block below by means of brass female screws let into it. They are the 
leveling screws of the instrument and are equidistant froin its center. 

Upon the underside and center of the metal lower disk is a socket containing a 
ball with a brass arm, which projects through the center of the block from beneath. 
The lower end of the arm is threaded, and upon it plays a female screw with a large 
milled head, which can be relaxed or tightened at pleasure. The screw clamps the 
whole upper part of the instrument to the stand; it is loosened only before leveling 
and kept securely clamped at all other times. 

The block, made either of wood or brass,* is supported upon three legs, and with 
them forms the tripod or stand of the instrument, the legs being of such a length as to 
bring the table to a convenient height for working, and so arranged as to be taken off 
at will, or closed so that their brass-shod and pointed ends can be brought together or 
moved outward, as may be required. They are made on the open or skeleton pattern, 
and each is securely attached to a segment of the tripod head by a long brass bolt. 

MOUNTAIN PLANE TABLE. 

A small plane table, with a board measuring only 14 by 17 inches, is employed in 
reconnaissance, mountain work, or as an auxiliary to one of the standard size. All the 
various parts are reduced in size to correspond with the board, and the construction of 
the movement simplified. 

The alidade. 

The type of alidade in general use (Illustration 3) consists of a skeleton rule (12 
inches long by 2^ inches wide) nickel-plated underneath, from and perpendicular to 
which rises a metal column (3 inches high), surmounted by Y's, receiving the trans- 
verse axis of the telescope, to one end of which axis is firmly attached a graduated arc 
of 30°, each side of a central 0°, an accompanying vernier being attached to the Y 
support. The arc moves with the telescope as it is raised or depressed, and it is used 
in the measurement of vertical angles to determine heights. A clamp and a tangent 
screw placed on the other side of the telescope, opposite the arc, controls its vertical 
movement. 

The telescope is fitted accurately near its center of gravity within a closely fitting 
cylinder, to which is solidly attached the transverse axis. The telescope revolves within 
the cylinder 180°, stops being fitted for that range. This affords an easy mode of 
adjusting the cross lines to the axis of revolution, and for correcting with a striding 
level the errors of level and collimation and revolution of the telescope. 

Upon the tube of the telescope are turned two shoulders, on which rest a striding 
spirit level, which can be readily reversed or removed at pleasure. The eyepiece 
carries the usual reticule with screws for the collimation adjustment, and to this is 
attached a glass diaphragm, having one vertical and three horizontal lines engraved 
upon it. One of the horizontal lines crosses the middle of the diaphragm, the other two 
are placed equidistant from it, one above and one below. The interval between them 
remains a constant chord for the measurement of distance upon a graduated staff or rod. 

* Now made of a special aluminum alloy. 



298 COAST AND GEODETIC SURVEY REPORT, 1905. 

In some cases short auxiliary lines have been added dividing the int /val into still 
smaller chords. 

Several of the alidades are furnished with a micrometer eyepiece so attached that 
the thread is horizontal, and has a vertical movement for measuring the angular distance 
of a fixed length on a rod which remains a constant chord. 

To the rule of the alidade are attached two spirit levels, one in the longitudinal 
direction of the rule and the other at right angles to it. 

A declinatoire (shown in Illustration i ) accompanies the alidade and is carried in 
the same packing box. It consists of a rectangular brass box 7 inches long by 2 wide, 
with an arc at each end graduated to 15° on each side of the 0°. It contains a needle 
long enough to extend from arc to arc, and resting on a pivot midway the box. The 
sides running lengthwise the box are parallel to a line connecting the zero marks of 
the two arcs. 

The metal clamps, for holding the projection on the board, are of two kinds: 
U-shaped for the ends, and the side clamps, the latter being made of thin metal strips 
about 12 inches in length, with two or more springs attached to grip the underside of 
the board. 

Adjustments. — From the nature of the service in some sections of the country the 
plane table is often necessarily subjected to rough usage, and there is a constant liability 
to a disturbance of the adjustments; still, in careful hands, a well-made instrument may 
be used under very unfavorable conditions for a long time without being perceptibly 
affected. One should not fail, however, to make occasional examinations, and while at 
work, if any difficulty be encountered which can not otherwise be accounted for, it 
should lead directly to an examination of the adjustments. 

1. The fiducial edge of the rule. — This should be a true straight edge. Place the 
rule upon a smooth surface and draw a line along the edge, marking also the lines at 
the ends of the rule. Reverse the rule and place the opposite ends upon the marked 
points and again draw the line. If the two lines coincide no adjustment is necessary; 
if not, the edge must be made true. 

There is one deviation from a straight line, which, by a very rare possibility, the 
edge of the ruler might assume, and yet not be shown by the above test; it is when a 
part is convex and a part similarly situated at the other end concave, in exactly the same 
degree and proportion. In this case, on reversal, a line drawn along the edge of the 
rule would be coincident with the other, though not a true right line; this can be tested 
by a true straight edge. 

2. The levels attached to the rule. — Place the instrument in the middle of the table 
and bring the bubble of either level to the center by means of the leveling screws of the 
table; draw lines along the edge and ends of the rule upon the board to show its exact 
position, then reverse 180°. If the bubble remains central it is in adjustment; if not, 
correct it one-half by means of the leveling screws of the table, and the other half by 
the adjusting screws attached to the level. This should be repeated until the bubble 
keeps its central position whichever way the rule may be placed upon the table. This 
presupposes the plane of the board to be true. The other level should now be 
examined and adjusted in a like manner. 



APPENDIX 7. A PIvANE TABLE MANUAL. 299 

Great care should be exercised in manipulation lest the table be disturbed. 

3. Parallax. — Move the eyeglass until the cross hairs are perfectly distinct, and 
th;n direct the telescope to some distant well-defined object. If the contact remains 
prrfect when the position of the eye is changed in any way, there is no parallax; but if 
it does not, then the focus of the object glass must be changed until there is no dis- 
placement of the contact. When this is the case the cross hairs are in the common 
focus of the object and eyeglasses. It may occur that the true focus of the cross hairs 
is not obtained at first, in which case a readjustment is necessary, in order to see both 
them and the object with equal distinctness and without parallax. 

4. Axis of revolution. — Since the bearings of the pivots are fixed, the axis of 
revolution is assumed to remain parallel to the plane of the rule. 

5. Vertical line of diaphragm. — Point the intersection of the vertical and the 
middle horizontal lines of the diaphragm on some well-defined distant object; revolve 
the telescope in its collar 180° and again observe the object. If the intersection covers 
it, the adjustment is perfect; if not, one-half the error must be corrected by moving 
the diaphragm, by means of the adjusting screws, and the other half with the tangent 
screw of the table. This operation should be repeated until the adjustment is perfect. 

6. Middle horizontal line of diaphragm. — (i) Adjust the striding level by reversing 
it end for end and correcting its error — half the difference by its own adjustment, half 
by the tangent screw of the telescope. 

(2) Point the telescope to a target, and note the reading, or make a mark where 
the wire points, when the bubble is in the middle. 

(3) Revolve the telescope in its collar 180°, and note the reading or mark the 
place where the wire points, when the bubble is in the middle. 

(4) The mean of the two pointings is the true level line, upon which the wire is 
to be adjusted, which may be done in this way: Keep the bubble in the middle and by 
means of the adju.sting screws bring the middle wire to bisect a point half way between 
the two readings or marks. The adjustment may be verified by revolving the telescope 
as in (2) and if the middle wire again bisects the point the adjustment is perfect. 

(5) If it is now desired to make the vernier read zero on the vertical arc, the table 
must be carefully leveled; and in order to do this more perfectly than can be done with 
the levels on the ruler, it may be done by observing the striding level; the telescope 
remaining clamped, the striding level should read the same in every position of the 
alidate when the table is perfectly level. (In general, this will be found too delicate a 
test, as the table is not sufficiently even for so sensitive a level to be employed.) The 
table being leveled, move the telescope with the tangent screw until the bubble is in 
the middle, and then set the vernier to read zero; the screw holes in it are oblong, so 
that it admits of being pushed either way. 

(6) It is easy to have the adjustments near enough to serve for running curves of 
equal elevation, but in determining the heights of stations it is best to make the obser- 
vations complete, with reversals, both of level and of telescope, taking the mean of the 
observations, by which the errors of adjustment are eliminated. This, in fact, is 
always done with the theodolite, and should be done with the alidade when precision 
is required. 



300 COAST AND GEODETIC SURVEY REPORT, 1905. 

The following may serve as an example: 

TEI,ESCOPE DIRECT. 

Reading of vernier, level direct with bubble in center 4, ^o , 

Reading of vernier, level reversed with bubble in center ^ 

Mean ~ ^ ~ 

Station, reading- T °„ ° '^ 

^ + 2° 17' 

Angle of elevation (difference) ... „ 

2° i6'.5 

TELESCOPE INVERTED. 

Reading of vernier, level direct with bubble in center - _ o / 

Reading of vernier, level reversed with bubble in center ....._ ^ 

Mean 

Station ~°° ^'-5 

■ • • • . +2° 12^ 

Angle of elevation (difference) 

2° i3'.5 

Mean 

2° 15' 

It will be seen, from analyzing these observations, that the level was one-half 
mmtite out of adjustment, the horizontal wire one and one-half minutes and that 
revolvmg the telescope in its collar 180° changed its relation to the index on the 
vernier by i'. The mean is free from all errors of adjustment 

TAe stadia rod^ (Illustration 3), used in the Coast and Geodetic Survey, is simply 
a scale of equal parts painted upon a wooden rod about 10 feet long, 4 inches wide 
and :.< inches thick, so graduated that the number of divisions upon it as seen 
between the upper and lower horizontal wires of the telescope when the rod is held at 
nght angles to the line of sight, is equal to the number of units in the distance between 
the instrument and the rod. 

Gra^^a/^b^ In all cases the rod should be graduated for the particular instru- 
^hllivlr '''"^'' ^'^ ^"^ ^^ ''^^^^°^^' ^° '"^' *^^ convenience of the 

In practice the alidade is mounted on a stand, and its center is plumbed over one 
end of a hundred-meter base, measured on level ground. A line, representing the zero 
of the graduation, having been drawn about 5 inches from one end of the rod, the latter 
IS held vertical at the other end of the base, zero mark upward. The obse;ver at the 
fnH . r.^ ! "fPP'' horizontal line of the diaphragm coincide with the zero 
and direc s the rodsman by signals where to draw a hue which coincides with the lower 
horizontal line. This intercepted space on the rod is subdivided to read meters and 
the graduation continued to within a short distance of the bottom. 

K^nZ^'i^^'^^r- 'J'i' °^ '^' '^'°''^ °^ '^'^^^ measurements see: Elemente der Vennessungs- 
fnd SlctroTr ■ ''' ir' '''"''"'^^ der Vermessungs-Kunde, Jordan, 1888, p. 5^ Theo^r^ 
and Practice of Surveying, Johnson, 1898, p. 238; Gillespie's Higher Surveying, Staley 1807 p Tn 

sers! VoTi N^? ^'^'^ ''^''°'^' '"^*'' """^*^° °^ ^"^^-^^^^ of'^.?;consin';'Eng-nLing 




y; 



/"A /'A 




U 






u 



M 



5i 



(L- 



8 



STADIA RODS. 



APPENDIX 7. A PLANE TABLE MANUAL. 30I 

This graduation is represented by the equation 

where cl=th.e distance from the center of instrument to rod (in this case 100 meters); 
/=the focal length of the telescope (which is 35"" for the average alidade); 
z=the distance between the upper and lower wires of the diaphragm (4""); 
5=the length of the intercepted portion of the rod (i"". 185); 

<:=the distance from object glass to center of instrument i = — ) 

As indicated in the preceding equation, the readings of a rod graduated in this 
manner are not quite true for distances above or below 100 meters, since the vertices of 
the constant and similar angles (one subtending the chord represented by the inter- 
cepted space on the rod and the other by the space between the upper and lower wires) 
do not lie at the center of the instrument, but at a distance beyond the object glass 
equal to the focal length of the telescope, and therefore the intercept on the rod will not 
be proportional for all distances from the center of the instrument. To have it so, the 
instrument should be mounted at a distance back from the end of the base equal to one 
and a half times the focal length of the telescope (/+0- 1*o all readings of a rod 
graduated according to this last method the constant quantity y+r must be added. 

The correction for the first method is small and can be ignored for mapping on a 
scale of I- 1 0000 or smaller. 

The formula for the correction is: 



Ar=(C+F) 



(■^0 



Where iT^ correction in meters, 

^= distance read on rod in meters, 

5' = length of base, in meters, for which the rod was graduated. 

The corrections for 50, 200, 300, and 400 meters are +0.262, —0.525, —1.050, 
— 1.575 meters, respectively. 

Inclined sights. — When the rod is held at a point above or below the instrument, 
the line of sight is inclined at an angle with the horizon, and a correction has to be 
applied to the reading to obtain the horizontal distance. If the rod is held perpendic- 
ular to the line of sight the reduced distance is simply the product of the cosine of the 
angle of inclination into the rod reading. If the rod is held vertical, which is the usual 
and also the safest method, there is an additional correction on account of the oblique 
view of the rod. These corrections can be ignored in the ordinary work of the Survey; 
that is, on a scale of i-ioooo or smaller, since for short distances they are too small to 
plot, and when the distances are long enough for them to become appreciable they are 
still small as compared to the uncertainty of the rod reading. 

For the convenience of the topographer engaged on large scale work, tables for 
reducing readings of inclined sights can be found at the end of the Manual. 

Micrometer eyepiece. — When a micrometer eyepiece is used in place of the stadia 
lines, a rod about 3.7 meters in length is employed, attached to which are two targets. 
A base is measured on level ground and the instrument either plumbed over one end or 
back of it a distance equal to f-\-c, depending upon the manner the rod is to be held 



302 COAST AND GEODETIC SURVEY REPORT, 1905. 

for an inclined sight. The rod is then taken to one of the subdivisions of the base, 
consisting of an even multiple of the unit adopted; say 100, 200, or 300 meters, and the 
upper target being fixed, the lower target is set and fixed so that the angular measure 
of the interval by the micrometer will consist of an even multiple of turns of the microm- 
eter screw. The rod is now held at the other subdivisions of the base, and the readings 
tabulated. A distance table is then prepared, by interpolation, for the intermediate 
distances. 

Plane-table sheet. — From the standpoint of efficiency the plane-table sheet is the least 
satisfactory portion of the plane-table equipment. Owing to its hygrometric nature it is 
very susceptible to atmospheric changes; expanding and contracting unceasingly. This 
would be but an insignificant source of error or annoyance if it were equal in all direc- 
tions. The map or plan would then simply change its scale, for which an allowance 
could readily be made. But the objectionable feature arises from the unequal expan- 
sion and contraction which changes the relative distance and directions of the points. 
It has been determined by experiment that strips cut longitudinally from drawing paper 
varied from 10 to 25 per cent more than strips cut transversely from the same paper. 

Various substitutes* have been tried, but none have proved entirely satisfactory. 
The United States Geological Survey, to eliminate this distortion, employs two sheets 
of paragon paper, the size of the plane-table board, mounted with the grain at right 
angles, and with cloth between them. 

This method is applicable to small scale surveys where a sheet the size of the table 
board covers a large area of country, or, on the other hand, to large scale cadastral sur- 
veys where the great amount of detail makes the rate of progress slow. But for inter- 
mediate scales and an area containing a moderate amount of detail, a longer sheet is 
much more economical, because a smaller number of points are needed to keep the 
work within the control of the triangulation than would be required if it was limited 
to the size of the table. A certain amount of overlapping work, of which there is more 
or less at the junction of the two sheets^ would also be avoided. 

The plane-table sheet of the Coast and Geodetic Survey consists of a sheet of 
Whatman's cold-pressed, hand-made antiquarian paper, 52 by 30 inches. It is backed 
with muslin, which extends about i inch beyond the edge of the paper to protect it 
from fraying. 

To reduce the distortion to a minimum a sheet should be thoroughly seasoned 
before it is taken to the field or a projection laid down on it. This is effected by 
exposing it alternately to a very damp and a very dry atmosphere. On testing a sheet 
after a week of such exposure it will be found to have much less tendency to expand or 
contract unequally. 

Paper stored away, piled up in stacks, does not properly season. 

Scale. — The selection of th^ scale to be employed depends so much on the char- 
acter of the country to be surveyed, the amount of detail to be included, and the uses 
to which the completed map will be put, that no general rule can be given for guidance. 
It must be remembered, however, that nothing is gained, either in economy or rapidity, 
by the use of small scales when the details are shown to be plentiful. The minute 
drawing involved proves a tax on the topographer and is a great time consumer. 

*Celluloid sheets are frequently used in Alaska. The pencil lines are neither washed out nor 
blurred by water accumulating on the sheet. 



APPENDIX 7. A PLANE TABLE MANUAL. 303 

The scale adopted by the Coast and Geodetic Survey for the coast line from Maine 
to Delaware Bay is i-ioooo; from Delaware Bay southward, 1-20000. Special surveys 
have been made on a scale as large as 1-1200. 

PROJECTIONS FOR FIELD SHEETS. 

It is presumed that determination has been made, by triangulation, of points most 
suitable for the use of the topographer who follows with the plane-table work, and that 
a sketch of the same is at hand, giving an approximate skeleton map of the area to be 
surveyed. The location or orientation (as it is frequently called) of the sheet is then 
based upon several important considerations. 

It may be taken as a rule that the intervisibility of the points extends across val- 
leys, from summit to summit, or across rivers, bays, and other bodies of water. So that 
generally the line of greatest depression of the valley (thalweg) should follow as nearly 
as practicable the middle of the sheet, regard being had for any abrupt change of direc- 
tion or importance of lateral features; or, in other words, the areas to be surveyed 
should be divided as far as possible into water basins, extending from divide to divide, 
and not center upon a ridge forming portions of two basins. The reason for this being 
that from either slope of the basin points are visible on the opposite summits which will 
be common to the sheets which include the adjoining valleys, while from the middle of 
the valley points will be visible on both summits. 

From the written descriptions of the points determined, discrimination should be 
made in regard to their temporary or permanent character. A flag in a tree is likely to 
have disappeared soon after its determination, and the usual cut of a triangle in its bark 
may have disappeared before the lumberman's ax, while a church spire, a light-house, 
a house chimney, a copper bolt in a rock, or a bottle buried beneath the surface of the 
ground is more likely to be recovered and to be of service to the topographer. 

Two intervisible points, one of which may be occupied, or three inaccessible points, 
are all that are absolutely necessary upon a sheet for the commencement of work, for 
from, or upon these, all other points required may be determined, and it is oftener 
more important, from considerations of economy of time and facility for work, to have 
more regard for embracing the topographical subject in its entirety, where points 
may be determined at convenience, than to furnish a large number of determined 
points at the expense of the best orientation of the sheets in regard to topographical 
details. 

In flat sections where the vertical question is scarcely a factor, the main ques- 
tion is generally a plan that will cover the area with the fewest sheets compatible 
with a sufficient overlap of common points; and where the object is a survey of one side 
of a river or other body of water, points on the opposite shore should be included when 
possible. 

When it is possible, the sheet should be located by one familiar with the peculiar 
topography of the region to be surveyed, and with some knowledge from observation 
of the relative value of the points between which there may be any necessity for 
discrimination. 

Where the surface is broken without any marked basins of large area, and when 
the sheet, on the scale determined upon, will cover several successive basins and divid- 
38077°— 16 2 



304 COAST AND GEODETIC SURVEY REPORT, 1905. 

ing ridges, the consideration of reach from higher to higher summits should control as in 
the reach over one valley ; thereby affording the best means for determining position and 
any desirable auxiliary points in the lower intermediate summits and in the valleys. 

Points at the junction of confluent streams have usually large arcs of visibility, and 
are consequently of great value for purposes of orientation. If, therefore, such a point 
should be near but off the edge of a sheet of regular dimensions, and from the necessi- 
ties at the opposite edge can not be included by it, it is often well to extend the length 
of the sheet so as to include the point, even though there may be no intention to com- 
plete topographic details upon the additional piece. 

Light-houses are often of this character, the reasons governing the selection of their 
positions for light purposes having equal weight in the selection of such positions for 
survey signals. 

The draftsman will be materially assisted in laying out the limits of the projection 
by drawing on a piece of tracing vellum a plan of the sheet, corresponding in size to the 
scale of the triangulation sketch. Take, for example, a sheet 52 inches in length by 30 
in width, on which a projection on a scale of i-ioooo is to be drawn, the triangulation 
sketch being on a scale of i-iooooo. The dimensions of the plan will then be one- 
tenth those of the sheet, viz, 5.2 by 3.0 inches. Placing the pattern over the sketch 
and shifting its position about over the locality to be surveyed, the limits which include 
the most favorable conditions for the projection will soon become apparent. 

The Poly conic projection * has been adopted by the Coast and Geodetic Survey for 
mapping its work. The method of constructing one is as follows: 

The limits of the sheet having been determined, the middle meridian A (see illus- 
tration 5) is located and drawn; then' its intersection with the most central parallel is 
found, and the perpendicular B erected there. 

Next turn to the page of the ' ' Tables for a polyconic projection of maps " f in 
which is given the degree of latitude which includes the limits of the sheet. In this 
instance the latitude is 40°, to be found on page 223 of the tables. The number of min- 
utes of latitude on the central meridian, above and below the central parallel, being 
known, take the corresponding distance from the column headed "Sums of minutes for 
middle latitude" and lay it off (C) above and below the central parallel, and with the 
same distance as radius, strike arcs D D D D above and below, from near the extremi- 
ties of the perpendicular B. With a well-tested straightedge draw lines E E through 
the north and south minutes on the central meridian, and tangent to the two arcs D D 
to the right and left. This gives three parallel lines perpendicular to the central merid- 
ian. On the opposite page 222, from under the head of ' 'Arcs of the parallel in meters, ' ' 
take out the value corresponding to the number of minutes of longitude east and west 
of the central meridian and lay off the whole distance F F' F" on each perpendicular, 
taking each distance from its appropriate latitude. Subdivide these into minutes 
G G' G". 

For the areas usually covered by plane-table sheets the corrections X, for deter- 
mining the abscissas from the arcs of parallels (Table VI, head " Coordinates of curv- 

* See a Treatise on Projections, Craig, United States Coast and Geodetic Survey 1882. Chart 
and Chart Making, Pillsbury, No. 29, Proceedings United States Naval Institute, 
t United States Coast and Geodetic Survey Special Publication No. 5, 1900. 



in 












O 












z 






UJ 








> 




Vs 
n 


*•« 








% 


«■ 


? °S j; ? 










If 








p 








i 




MS 




ttiS 


- 




























/I 


i 








ii 








II 










1 








1/ 










1 
1 1 




y- 


> 


1 1 

' 1 










ri 








1 1 
1 1 




P 




. 1 
1 1 








h 
1 1 








1 








1 1 






a I 






1 








1 1 




-6 1 






1 








1 1 






k£> 






1 
1 








1 




"i 






\ 
\ 








1 




!?> «3 






\ 








/ 


- 


I'S 




v^ 






\ H 


O! 1 






1 
1 






/r^^ 

' 


1 
\ 

1 
1 


. 


1^ 

iC ^P 




1 




1 




If 














II 




^^§ 










1 
\ 








s ^ ^ 




Z 


1} 




-J - * 


^ 

' 


. ^i 


</) 


fl\ "^ ^ 






:~ J -i,— r^ 


^ -'' 


*1 








^^z- " 










^M 








s 


S 


■p 


l-l 




gra.rri' illustrating 

conto Projectiort fo 

Scale of I) 










,1 














ill 






























1 
1 


1o 
















1 

1 


«> 
^ 


^ 




- 










1 


«o 






» 






c-^ 


1 
If 






1 








'! 
1 


f 






I 






u 




E 


^ 








1 










^ 








fP 




1 


^\ 


« 
^ 










^ 







APPENDIX 7. A PLANE TABLE MANUAL. 305 

ature " ), are inappreciable and may be disregarded, the ordinates Y only being used. 
These give the distances to be set off from the lines B and E, perpendicularly toward the 
pole, for each minute of longitude counting from the central meridian. For ordinary 
field projections of scale i-ioooo the ordinate of the extreme minute only need be used, 
and the parallel drawn a right line from the point so found to the central meridian. 
This ordinate H being set off on each of the parallels, the meridians are all drawn in 
with a fine ruling pen, then subdivided into minutes, and the parallels carefully ruled 
in through the points of subdivision. 

The projection is verified by applying the measure of a number of minutes of lati- 
tude and longitude, and by a comparison of diagonal measurements on different parts 
of the sheet. 

All measurements should be carefully taken from the scale with a keenly pointed 
beam-compass, and the marks pricked in the paper should be as light as possible to be 
seen, so as to insure the greatest possible accuracy. 

The draftsman is supplied with a list of triangulation points, which gives their rel- 
ative distances, their latitudes and longitudes, and also the equivalents in meters of the 
seconds of latitude and longitude, according to which the points are now plotted on the 
sheet by measuring from the corresponding minutes. Thus in the diagram the distance 
J represents the seconds of latitude; K, the seconds of longitude of the trigonometric 
point. 

The accuracy of the plotting is tested by a measurement of the respective dis- 
tances between the points with a beam-compass, these distances being also given. The 
latitude and longitude are then plainly marked, usually on the north and east sides of 
the sheet, at one extremity of each parallel and meridian, and the pencil marks erased. 

It sometimes becomes necessary to base topographic work upon a detached scheme 
of triangulation, before the usual astronomic observations have been made. In this 
case the only elements given are the distances from the points to two projected arcs of 
rectangular coordinates (which are assumed) and the distances between the points. 
The projection for plotting these consists simply of axes of ordinates and abscissas so 
laid on the sheet that it will embrace all the points required by the surveyor, and in the 
manner most convenient for his work; and the points are plotted from these by the 
intersection of two arcs with the distances of the points from the axes as radii, either 
north or south, east or west of the axes, as the plus or minus sign given may indicate. 
The only test is by the distances between the points, and there should be at least two 
from each. If the work be correctly done, a regular projection can be constructed on 
the sheet after it is finished and the required astronomic work is completed. 

In case it so happens that for some special purpose it becomes urgent to undertake 
a piece of topography, when neither the data for projections nor coordinates are at 
hand, plotting by distances is the only resource left, and, of course, great care is 
necessary. 

When a sheet has no projection — that is, no meridians and parallels, it is advisable 
to draw squares of i 000 or any specified number of meters on it, by means of which 
the projection can ultimately be laid down correctly. 

Accessories. — The usual accessories for plane-table work are: Large umbrella for 
shading table, binocular, pocket compass, 10 or 20 nieter steel tape, Locke's level, 



3o6 COAST AND GEODETIC SURVEY REPORT, 1905. 

clinometer, metal scale, dividers, pencils, rubber, block of emery or sand paper, table 
of heights, note, and sketch book.* 

A metal chart case should always accompany the table to secure the sheet from 
sudden rain and other injury liable to occur in transportation of the sheet to and from 
the field and for its safe-keeping when not in use. Its diameter should not be less than 
3 inches, for no sheet can be rolled to a less diameter without serious rupture of the 
fiber of the paper. It is also advisable to have a rubber cloth for covering the table 
when it is carried from station to station. 

Approximate weights. — Plane-table movement, 18^ pounds, boxed, 34 >^ pounds; 
plane-table board, 8^ pounds, boxed, 26^^ pounds; plane-table alidade, 7 pounds, 
boxed, 21 J4! pounds; plane-table tripod legs, 11 pounds; 2 stadia rods, i6>^ pounds. 
Mountain plane table, set up complete with alidade, 19^ pounds, boxed, 36 pounds; 
2 stadia rods, 12^ pounds. 

Field Work. 

Organization of party. — In organizing a party for field work it is necessary to have 
one man to carry the table. His duty is to remain constantly with the instrument, 
never to leave it unguarded ; and while the topographer is at work he holds the umbrella 
to shade the table from the sun and thus protect the observer's eyes from the glaring 
reflections from the paper and instruments. The table bearer should be taught at the 
beginning of the work the mode of setting the table over a point and taking it up from 
the same. In the first instance to grasp firmly two legs of the tripod and with the 
knee to extend the third one until it reaches the ground at the proper distance from the 
point, and then place the other two in position. The distances from the point will 
vary, as the ground may be level or sloping, in order to keep the tripod head vertically 
over the point and approximately horizontal, .securing the latter condition by sighting 
over the head to the horizon. In taking up the table two legs should be grasped 
firmly and the table raised, resting upon the other leg, upon which the first two are 
closed, when the table is raised in place upon the shoulder. 

Two rodsmen are needed, and the rapidity with which the work is executed largely 
depends upon their efficiency. When well trained they should be able to recognize the 
salient points of the features to be mapped, so that the topographer can draw in correctly 
the details from the least number of readings, in the absence of an aid to make a sketch 
of the intricate portions. 

The amount of assi-stance an aid can give to his chief is hmited only by his skill 
and experience. The logical inference being that he is in training to become a topog- 
rapher himself, he takes charge of an increasing share of the work as he becomes more 
and more familiar with the methods employed. This enables his chief to turn his atten- 
tion in other directions, which will expedite the survey and increase the output. 

An outline, merely, of his duties can be suggested: Building signals, drawing plans 
of intricate details, sketching contours, selecting stations in advance, running traverse 
lines with auxiliary instruments, and finally in taking charge of the plane table in the 
absence of his chief, who is thus afforded the opportunity of inspecting some difficult 
area and formulating some plan to meet the conditions found there. 



*For the Locke's level, clinometer, and pocket compass a Casella pocket alt-azimuth instrument 
may be substituted, as it combines all three in a very convenient form. 



u 



NO. 6. 



'i aCkimTtey 



Fig.l 




Rg. 2 



^±-.^..^,.. 


T 




-i 



fe^ 



~'~-l 



B\ 



■•^B 





^x i 


[ \ 








^^^OCL ^\\\s 


/ / 




Fig. 3 


^"^^v^N^ \ \ 


// 






^n\ \ / 


ac 


p1 






n 




T"' 








\ l\ 




H 1 



GRAPHIC TRIANQULATION. 



APPENDIX 7. A PLANE TABLE MANUAL. 307 

The additional number of men required to complete the party will depend mainly 
on the means of transportation — wagon, horseback, or boat. 

Preliminary reconnaissance. — Before commencing the instrumental work, a recon- 
naissance of the country should be made for the purpose of recovering triangulation 
stations and to locate signals at suitable points for subsequent determination and use. 
In the location of signals, either as permanent points or simply for temporary forward 
lines, a great deal depends upon the good judgment of the person placing them. Two 
purposes are to be subserved: First, the seeing of sufficient known points to give a good 
determination; and, second, to command a view of as great an area of country, and as 
many natural and artificial features for filling in the topography, as possible. It should 
be remarked, also, that in the course of prosecution of the regular work no favorable 
opportunity must be allowed to pass for locating a signal or determining a point which 
may at some future time be of service. Advantage should be taken of open places in 
the woods commanding roads or ravines. Piers or draws of bridges, or piles, giving lines 
up and down streams, which have precipitous and wooded banks; trees of unusual 
appearance in prominent positions, or bearing flags placed upon them for the purpose; 
points of rock, offshore or otherwise; lightning rods, cupolas, weathercocks, chimneys 
of factories, and other peculiar and marked objects come within this category. In fact, 
it may be set down as a rule that well-determined signals located at convenient distances 
over the sheet are more likely to be too few than too many. 

Signal poles should be straight and perpendicular, and the flags upon them adapted 
in color to the background against which they will be seen when observed upon. 

Graphic triangulation (Illustration 6). — Signals having been erected at each trian- 
gulation station, and also on all prominent hills within the area of the sheet, where they 
will be useful in providing additional control, the next proceeding will be to occupy 
one of the former points. 

Care should be exercised in choosing a day for this portion of the work, as it is 
essential to have favorable weather for a satisfactory test of the plotted points in the 
field and for the determination of new ones. 

On arrival at the station the table is set up approximately over the center mark, 
and the sheet secured to the table, so that it will be held firmly and evenly and not be 
disturbed in its position by the friction of the alidade, nor by ordinary winds. As the 
longest side of the board is usually made equal to the width of the sheet, and the sheet 
is usually longer than this width, the excess of length is rolled up inward, turned under- 
neath the sides of the table and fastened with a metal spring clamp, biting from the top 
of the sheet on the table to the inside of the roll beneath. One clamp at each end of 
the roll serves to hold the roll ends securely. The sides of the sheet are sometimes held 
to the table by similar but shorter clamps, but it is preferable for the free movement of 
the alidade, and more secure against strong winds, that a metal strip, the length of the 
side between the end clamps, with spring clamps fastened to the outer edge, and biting 
the underside of the table, be used for holding down the edges of the paper. 

The chief and controlling condition in work with the plane table, and without which 
no accurate work can be done, is that the table shall be oriented — that is, that all lines 
joining points on the sheet shall be parallel to the corresponding lines of nature. 

Let T, T', T", T"' (Fig. i) represent the board of the plane table, upon which is 
spread the sheet; the plotted triangulation point a upon the sheet representing the 



3o8 COAST AND GEODETIC SURVEY REPORT, 1905. 

signal A upon the ground; b, the spire B; r, the signal C; and p, the station P; the 
small letters on the sheet representing the centers of the signals on the ground, which 
are referred to by corresponding capital letters. / 

The table is placed approximately level over the station occupied, P, and oriented, also 
approximately, by the eye, so that the plotted points on the sheet are in approximate 
range with the station P and the signals or objects they represent in the field. Then 
plumb the point /> over the station P, fixing the legs of the table firmly in the ground. 

In maps of large scale it is important to plumb the plotted point exactly ovei* the 
station, but on the usual field scales of the Coast and Geodetic Survey (i-ioooo and 
1-20000) an approximation with the eye is all that is requisite. To effect it more 
closely a small stone is held underneath the point and then dropped to test the position, 
or a plumb bob fastened to the table below the point serves the same purpose. Plumb- 
ing arms or forks are made and supplied by the instrument dealers. 

The plotted point having been plumbed over the station as accurately as the scale 
of the work demands, place the alidade on the table so that the rule shall extend across 
and parallel with the line joining two of the leveling screws; loosen the large clamp screw 
under the tripod head, and with the leveling screws bring the bubbles of the two levels 
on the rule to the center; clamp the screw under the tripod head, and the table is level. 
Now, unclamp the revolving plate, place the edge of the rule upon the plotted points/ 
and b, the telescope being directed toward the spire B, as shown by the arrow-head of 
the figure, and revolve the table until B is seen in the field of the telescope; clamp the 
revolving plate, and with the tangent screw of the movements bisect the top or center 
of the spire B with the vertical wire of the telescope. The table is now oriented, if the 
points have been correctly plotted and the proper objects sighted. To verify this, place 
the rule upon the point/ again, and upon the points a and c, consecutively, and if the 
two signals A and C are bisected by the vertical wire of the telescope, the position is 
assured, and the lines connecting points of the sheet are parallel with the corresponding 
lines on the ground. 

The failure to bisect A and C would indicate an error of plotting or an unequal 
change of the dimensions of the paper (distortion), which must be examined, and in 
case of the former, corrected, and in case of the latter, allowance made for, as indicated 
later on. (See distortion errors, page 316.) 

The next proceeding is to draw the line to the next point which it is desirable to 
occupy or determine, either some natural object which can be occupied, or a temporary 
signal placed for that purpose, as the signal D. 

The edge of the rule is placed upon the point /, and moved about that point as a 
center until the signal D is bisected by the vertical wire, and then a line, f, is drawn 
along the edge of the rule from / far enough to reach the estimated position on the sheet 
of the point d, and at each end of the rule the short check lines n n are drawn. These 
check lines can be used in reversing the alidade with the accuracy that is obtained by 
the greatest length of a range line. They may be indicated on the sheet, with names 
of objects, as in fig. 2 — ch., chimney; /., tree; cup., cupola; sp., spire; w. th., windmill; 
or numbered, and a record kept of the objects sighted, where details are complex. 

In the same manner lines should be drawn to such objects as it is desired to deter- 
mine. This determines only the one element of direction; it will be necessary to 
determine the distance from the point occupied either by measurement or by intersec- 



APPENDIX 7. A PLANE TABLE MANUAL. 309 

tion from some other fixed point, at an angle not less than 30° nor more than 150°; 
all acute intersections should be verified by a direction from a third point. 

The table is moved to the station A (Fig. 2) and placed over the point, oriented 
approximately, leveled, and the axis of revolution clamped as at station P. The rule 
is then set upon the line a p, the telescope directed toward the signal P, and the table 
put in position in the manner described. Then, keeping the edge of the rule upon 
a, direct the telescope to the signal D and draw the line a d, intersecting f, and deter- 
mining the position of the point d upon the sheet, corresponding to D, and bearing the 
same relation in directions and distances from the points p, a, b, and c as the signal D 
does from P, A, B, and C. All lines to other objects which were drawn from p, and 
which objects can be seen from A, are intersected and determined in the same manner. 

When a direction has been drawn from a station to any undetermined point that 
may be occupied, the position of the point may be determined by occupying it with the 
table, and orienting the table by the line drawn to it, and resecting upon a signal whose 
corresponding point is plotted upon the sheet. 

The table is placed over the point D (Fig. 3), oriented approximately, leveled, 
etc., as at the previous stations. The edge of the rule is then placed upon the line dp, 
passing through the point p, so that the checks n n are just visible along the edge, and 
the telescope directed toward the signal P, and the table oriented. The rule is then 
placed with its edge bisecting one of the plotted points, such as b, which will give a good 
intersection (the nearer 90° the better) with the line f, and is moved about that point 
as a center until the spire B is bisected by the vertical web. A line is now drawn accu- 
rately along the edge of the rule through b, crossing the liney". If this line intersects the 
line /at the point d, the position of the latter is assured, and a delicate hole with the 
dividers should be pricked at the point, surrounded by a small circle in pencil. 

Resection upon any other determined point will verify its position. 

From this point, d, directions are observed and drawn to verify the previous inter- 
sections upon chimney, tree, cupola, windmill, etc. 

There are occasions when occupying some station that several objects are seen 
whose position it is desirable to determine by prosection, but there is doubt of their being 
recognized from other stations. A new station is then occupied close by the first one 
and new lines drawn to the objects. The intersection thus obtained will necessarily be 
acute, but will materially assist in their identification from other localities. 

All lines should be drawn lightly and carefully, close to the edge of the rule, with 
a hard, finely-sharpened pencil. If the table and alidade be in proper condition, the 
contact of the edge of the rule with the paper will be perfect throughout its length, 
and in drawing a line along the edge care must be taken to preserve the same inclination 
of the pencil and to keep it sharp. If the rule should be raised from the paper at any 
part, great care is to be observed that the pencil does not run under the edge and thus 
deviate from a straight line. 

Amount of control. — There is no fixed ratio between the number of determined 
points and the number of square miles of the region to be surveyed or square inches of 
plane-table sheet. 

The greater the number of points well distributed over the latter the less likelihood 
of error due to distortion of the paper. 



3IO COAST AND GEODETIC SURVEY REPORT, 1905. 

A large number also makes it easy for the topographer to determine by resection 
subordinate stations for mapping the details, and in consequence fewer traverse lines 
need be run. / 

More than sufficient for these purposes are not necessary, and it is important when 
carrying on a graphic triangulation not to waste valuable time and favorable weather, 
but to advance this part of the work as rapidly as possible before the sheet becomes 
affected by exposure. 

The three-point problem (Illustration 7). — A subordinate station is located at any 
desired place where a good view of the surrounding features can be obtained. If the 
position of this point has not been previously determined it is now effected by means 
of the resection of lines from three fixed points. 

The special advantages of the plane table as a mapping instrument are due to the 
rapidity with which it obtains results by the method of graphic triangulation and to 
the facility it affords the topographer in determining his position at an unknown point 
by the graphic solution of the three-point problem. 

When the latter method is applicable — that is, when the country is open and signals 
can be easily seen — its superiority over a system of traverse lines is manifest. The 
topographer is then at liberty to choose his ground without reference to his last station 
or to one succeeding. He is not tied down to a backsight nor restricted by the condi- 
tions imposed by a foresight. He need not set up his instrument on an area barren of 
detail nor cut his way through obstacles (bushes, hedges, trees) to establish a station 
at a commanding point of view. 

The number and situation of the stations are governed solely by the amount and 
location of the information to be mapped. On the other hand, traverse stations are 
chosen on account of their visibility, and many of them are of no service whatever 
beyond carrying the line forward. 

When the table is imperfectly oriented, the lines drawn from the three projected 
points, when sighting on the corresponding actual points, will not intersect at one point 
unless all four are on the circumference of a circle. (See Fig. 3, Indeterminate posi- 
tion.) Except in this case, two of the lines will be parallel, intersected by a third 
(see Fig. 4, Station on range line between two fixed points, and Fig. 2, Station on pro- 
longation of range line), or they will form a small triangle called the triangle of error. 
(Figs. I, 3, 5, and 6.) The solution of the three-point problem determines the location 
of the station occupied and orients the table simultaneously. 

The relative positions of the three fixed points with reference to the new station have 
an important bearing on the strength of its determination. 

In the following statement in regard to the different groupings of points met in 
practice, for the sake of brevity, the term " fixed points " will be understood to mean 
points already determined and plotted on the sheet; the "great triangle" referred to 
is one formed by the three fixed points, and the ' ' great circle ' ' is the circle passing 
through them. 

When the new station is outside the great circle, the strength for determination of a 
position will be weak when the middle point as seen from the new station is the farthest 
of the three and the angles are small. (See Illustration 7, Fig. 3.) If the new sta- 
tion is located outside the circle, and some distance below it, the angles are small and the 
determination correspondingly weak. 



NO. 7. 




Triangle of error 



Yig.\ 




Point sought 



Indeter- ^ 
minale ,>^ ^S^. 




Sl^Trbdeterminate 



Triangle 



Searijent \ 



V Indeterminatfe r 

\ In.dye terminate / 



\D 



^-^^eat circ^^-' 



b 



a 

-A- 




QPoint souxjhl. 



Fig.6 




d Point sovighz 



Fig. 



-^ 



AC 



Fig. 3 



a, 
A 




^ Bange line 



A 

Point sought "^ 



Fig. 4 



'oint sought 




Fig. 5 



THE THREE-POINT PROBLEM. 



APPENDIX 7. A PLANE TABLE MANUAL. 3 1 1 

The determination increases in strength for given angles as the middle point 
approaches the new station. (Fig. i.) 

When one angle is small or 0° (points in range), the determination will be strong, 
provided the two points making the small angle or range are not too near each other 
when compared to the distances to the new station and to the third point; provided also 
the angle to the third point is not too small. (Fig. 2.) 

When the new station lies on or near the great circle, its position is indeterminate. 
(See Illustration 7, Fig. 3.) 

When the new station is mithin the great circle, the strength of its determination 
increases as it approaches the center of gravity of the great triangle. (Figs. 3, 4, 5.) 

There are a number of graphic solutions, but all save three are better suited to the 
drafting room with its appliances than to the conditions which exist in the field. 

Lehmami's method of solution is the simplest and most direct, and applies under all 
circumstances. The directions are stated in the form of rules. 

The term ''point sought" will be understood to mean the true position on the 
sheet of the projected point of the station occupied. The surveyor is assumed to be 
facing the signals, and the directions right and left are given accordingly. 

Rule I. — The point sought is always distant from each of the three lines drawn 
from the three fixed points in proportion to the distances of the corresponding actual 
points from the vStation occupied,* and it will always be found on the corresponding 
side of each of the lines drawn from the fixed points. f 

The simplest case for the application of this rule occurs when the station to be 
determined is within the triangle formed by the three fixed points; the point sought 
must then be within the triangle of error to satisfy the conditions. (See Illustration 7, 

Fig. 5-) 

Although Rule i is sufficient in itself for the solution of the problem, there are two 
subordinate rules which materially assist the topographer in reaching a decision as to 
the proper location of the point sought with reference to the lines from the fixed points. 

Rule 2. — When the point sought is without the great circle it is always on the same 
side of the line from the most distant point as the intersection of the other two lines. 
(See Illustration 7, Fig. i.) 

Rule 3. — When the point sought falls within either of the three segments of the 
great circle formed by the sides of the great triangle the line drawn from the middle 
point lies between the point sought and the intersection of the other two lines. (See 
Illustration 7, Figs. 3, 4, 6.) 

Application of rules. — In practice the topographer first decides the relation of the new 
station with reference to the fixed points, whether it is within the great triangle or in 
one of the segments or outside the great circle. He then determines the position of the 

* Demonstration. — A,-B, C (Illustration 8, Fig. i) are projections of the three signals from which 
it is desired to determine by resection the position of a fourth point, D. The table being out of posi- 
tion to the right, the triangle of error formed by the three lines from A, B, and C is ab, ac, be. The 
true point occupied lies at D, being at the intersection of the circles AB ab, AC ac, BC be. Now, if 
perpendiculars be drawn from D to the lines drawn from A, B, and C, we shall have 

Da : Db :: DA : DB or Db : Dc :: DB : DC. 

t That is, if it is on the right side of one line, it is on the right side of each one of the other two, 
and if on the left side of one, it is on the left side of each one of the other two. 



312 COAST AND GEODETIC SURVEY REPORT, 1905. 

point sought with reference to one line (if within one of the segments or without the 
great circle by Rule 2 or 3); it then follows from Rule i that it must be on the corre- 
sponding side of the other two lines. Finally, he estimates the relative distances of the 
three actual points from him and marks the position of the point sought a proportionate 
distance from the three lines. ^ 

EXAMPLES. 

Illustration 7, Fig. i: When the point sought is without the great circle, the inter- 
section of the lines from B and C fall to the right of the line from A, the most distant 
point; therefore (Rule 2) the point sought must be on its right, and also (Rule i) on 
the right of the line from B and C. Its exact position is then estimated according to 
Rule I. 

Illustration 7, Fig. 2: When the point sought is on or near the prolongation of a 
range line, it must be outside the parallel lines on the side of the line to the nearest 
fixed point of the range. In the figure it will be seen that the point sought must be 
outside the lines from A and B, and to their right to satisfy Rule i, and also to the 
right of the line from C. 

Illustration 7, Fig. 3: When the point sought is on the circle passing through the 
three fixed points, the position is indeterminate, as the three lines will intersect at one 
point, although the table is imperfectly oriented. Another selection of points must be 
made. 

Illustration 7, Fig. 3: When the point sought falls within one of the segments of the 
great circle, the line drawn from A, the middle point is to the right of the intersection 
of the lines from B and C; therefore (Rule 3) the point sought must be on its right 
side, and also (Rule i) to the right of the line from B and from C. Locate it exactly 
according to Rule i . 

Illustration 7, Fig. 4: When the point sought is on or near the range line between 
the fixed points, the point sought must be between the parallel lines to satisfy the 
conditions of Rule i . Its position with reference to the intersecting line follows from 
the same rule. In the figure the point sought being between the lines from B and C, is 
to the right of each, therefore it is to the right of the line from A. 

Illustration 7, Fig. 5: When the point sought falls within the great triangle, it 
must fall within the triangle of error. No other position would satisfy the conditions 
of Rule I. 

Illustration 7, Fig. 6: When the three fixed points are in a straight line. In this 
case the points are considered as being in the circumference of a circle of infinite diam- 
eter and the point sought always lying in one of the segments of the great circle. The 
treatment of this case is then identical with that of Illustration 7, Fig. 3. 

The preceding cases are all examples of the conditions which may occur when the 
table is deflected to the right. By turning the printed side of the illustration to the 
light and looking at the figures through the paper, they will appear reversed, and they 
will then be examples of conditions which may occur when the table is deflected to the 
left. 

Repetition. — When the true point has been estimated and marked on the sheet in 
accordance with the foregoing rules, a new orientation is made. If the lines from the 
three stations now intersect at that point, it proves the estimate to have been correct 



..j9 




Pig.l 




Fig.2 





Fig. 6 




Fig- 3 




THREE-POINT AND TWO-POINT PROBLEMS, 




BESSEL'S SOLUTION OF THREE-POINT PROBLEM. 



APPENDIX 7, A PLANE TABLE MANUAL. 313 

and the position is determined. If a new triangle of error is formed, it indicates an' 
erroneous estimate, and the operation must be repeated. 

Orienting by estimation. — A small triangle of error is the result of a close orienta- 
tion, which the topographer endeavors to accomplish at the first trial by taking advan- 
tage of any range that may exist either of signals or other details already plotted on 
the sheet. It will serve the same purpose if they are near enough in line to estimate a 
direction on the sheet to the farthest object, and then to orient by it. 

The declinatoire may be used, but it is a slow and inaccurate method of orientation. 

It is employed for this purpose by placing the straight edge of the box containing 
the needle upon a magnetic meridian, previously traced upon the map, and revolving 
the table until the needle points to 0°, or north, on the graduated arc at the end of the 
box. The magnetic meridian is roughly determined at any well-determined station, 
when the table is properly oriented by the use of the declinatoire itself, the meridian 
line being drawn upon the sheet along the straight edge of the box when the needle 
points to 0°. Or the table may be oriented by making the straight edge of the box 
coincide with one of the meridians of the projection and then turning the board until 
the needle points to the right or left of the zero, according to the amount and direction 
of the magnetic deviation. 

BessePs method by inscribed quadrilateral is the simplest method by construction. 
The objection to it arises from the fact that in practice the intersection of the construc- 
tion lines often falls beyond the hmit of the board. 

By this method a quadrilateral is constructed with all the angles in the circumfer- 
ence of a circle, one diagonal of which passes through the middle one of the three fixed 
points and the point sought. On this line the alidade is set, the telescope directed to 
the middle point, and the table is in position. Resection upon the extreme points inter- 
sects in this line and determines the position of the point sought. 

Illustration 9, Figs, i, 2, 3, and 4. Let a b c\i& the points on the sheet represent- 
ing the signals A B C on the ground. The table is set up at the point to be determined 
(a?), and leveled. The alidade is set upon the line ca, and a directed, by revolving the 
table to its corresponding signal A, and the table clamped; then, with the alidade 
centering on c, the middle signal B is sighted with the telescope and the line ce drawn 
along the edge of the rule. The alidade is then set upon the line ac and the telescope 
directed to the signal C, by revolving the table, and the table clamped. Then, with 
the alidade centering on a, the telescope is directed to the middle signal, B, and the line 
ae is drawn along the edge of the rule. The point e (the intersection of these two lines) 
will be in the line passing through the middle point and the point sought. Set the 
alidade upon the line be, direct b to the signal B by revolving the table, and the table 
will be in position. Clamp the table, center the alidade upon a, direct the telescope to 
the signal A, and draw along the rule the line ad. This will intersect the line be at the 
point sought. Resection upon C, centering the alidade on c in the same manner as 
upon A, will verify its position. 

The opposite angles of the quadrilateral adce being supplementary, 

Aace and Z.ade are subtended by the same chord ae, and Acae and Acde are sub- 
tended by the same chord ce; consequently, the intersection of ae and ce at e must fall 
on the line db; or, the segments of two intersecting chords in a circle being reciprocally 



314 COAST AND GEODETIC SURVEY REPORT, 1905. 

proportional, the triangles adf and cef are similar, and the triangles cdf and aef are 
similar, and d,f, and e must be in a right line passing through b. 

In using this method the triangle formed by the three fixed points can be contracted 
or extended, as may be desirable, by drawing a line parallel to the one joining the two 
extreme points, and terminated by those joining the extremes with the middle^oint. 
The graphic solution can then proceed in the same manner as that described for an orig- 
inal triangle. 

Tracing-cloth protractor. — The third method consists in laying off the angles between 
the three known points on tracing cloth or paper, and using this as a protractor, deter- 
mine the position of the unknown point. 

Fasten a sheet of tracing cloth or paper to the board, marking upon it a point to 
represent the unknown point. Draw through it lines toward the three known points. 
Then shift the tracing cloth over the sheet until each of the three lines passes through 
the plotted point corresponding to the point toward which it is drawn. The position of 
the unknown point will be at the intersection of these lines. 

This method is less exact and not so convenient as the other two previously described, 
and is impracticable when the wind blows. 

TWO-POINT PROBLEM. 

The occasion may arise where it is desirable to place the table in position at a given 
point, from which only two determined points are visible. This may be done by the 
following methods: 

One method possesses the virtue of requiring no linear measurements, and demon- 
strates in a very satisfactory manner the effectiveness of the table in determining posi- 
tion by resection. 

(Illustration 8, Figs. 2,3,4 ^'^d 5- ) ^ Two points, A and B, not conveniently access- 
ible, being given, by their projections a and b, to put the plane table in position at a third 
point, C. (The capital letters refer to points on the ground, and the small ones to their 
corresponding projections.) 

Select a fourth point, D, so that the intersections from C and D upon A and B 
make sufficiently large angles for good determinations. Put the table approximately in 
position at D, by estimation or by compass, and draw the lines Aa and B^, intersecting 
at d; through d draw a line directed to C- Then set up at C, and assuming the point c on 
the line dQ., at an estimated distance from d, and putting the table in a position parallel 
to that which is occupied at D, by means of the line cd, draw the lines from c to A and 
from c to B. These will intersect the lines dK and dV> at points a' and b' , which form 
with c and d a quadrilateral similar to the true one, but erroneous in size and position. 

The angles which the lines ab and a'b' make with each other is the error in posi- 
tion. By drawing through c a line cd' making the same angle with cd as that which ab 
makes with a'b' , and directing this line cd' to D, the table will be brought into position, 
and the true point c can be found by the intersections of aA and (5B. 

Instead of transferring the angle of error by construction, we may conveniently pro- 
ceed as follows, observing that the angle which the line a'b' makes with ab is the error 
in the position of the table. As the table now stands, a'b' is parallel with AB, but we 
want to turn it so that ab shall be parallel to the same line. Place the alidade on a'b' 



APPENDIX 7. A PLANE TABLE MANUAL. 315 

and set up a mark iu that direction, then place the alidade on ab and turn the table 
until it again points to the mark, then ab will be parallel to AB, and the table is in 
position. 

Another method is as follows (Illustration 8, Fig. 6): 

Two points, A and B, not conveniently accessible, being given by their projections 
a and b, to put the plane-table in position at a third (undetermined) point, C. 

Set up the table at the point sought as closely oriented as can be done by estimation, 
and resect upon A and B, intersecting the line be at c' . The angle ac'b is the true 
angle at the point occupied, subtended by AB, being the angle of nature actually drawn; 
therefore, the true point must be on the circumference of the circle passing through abc' . 
Construct this circle. Measure off a base, CD, at least half the length of CB, at right 
angles, or nearly so, to be, in either direction most convenient. Set up a signal at D,! 
and with the alidade draw the line e'd. Remove the table to D, and, by means of ^ 
signal at C (the point sought), and the line de\ bring the table into a position parallel 
to that which it occupied at C. With the alidade centering on d, observe the signal B, 
and draw the line db' intersecting cb at b' . e'b' is the distance of the point C from B; 
and this distance laid off on the circle ae'b as a chord from b will give e" , the true posi-: 
tion of the point C. A fourth point may then be occupied, and bj^ resection upon A,; 
B, and C the accuracj^ of the determination of C verified. : 

Where it is possible to get the two signals A and B in range, it is easy to determine 
the position of a third point by a method long practiced by topographers. 

Set up the table anywhere on the range line, and orient by the latter. Resect on 
the unknown point, drawing the line an3'where on the .sheet most convenient. Leave a' 
signal at the occupied point on the range line and set up the instrument at the unknown 
point. Orient b}' the line drawn when at the station on the range line, sighting on the 
latter station. The table will now be in a parallel position to that when on the range 
line, which is the true position, and the unknown point maj' be determined by resec- 
tion upon the two fixed points and their projections. 

Deflection of long lines. — In adjusting lines of intersection upon a point or object! 
from a series of stations, when these lines do not coincide in one point, as they are 
usually derived from signals at unequal distances, the error should not be divided equally 
among them, but in proportion to their lengths if the discrepancies are not eliminated 
by the rules for distortion errors given later. 

It should be borne in mind that very short lines from a determined point — as, for 
instance, to the corners of a fenced road, where the table occupies the center of the 
intersection of two roads — may be taken with no apparent error when the table is 
deflected to .some extent from its true azimuth, but that in this case a prolonged line 
will be considerabl}' out at its further extremity. 

A long line should never be obtained by the prolongation of a short one from a back 
station where there is no small check line, or some other point in that prolongation 
already fixed. 

It will be apparent that the more nearly at right angles intersecting lines cross each 
other the more clearly the point will be defined; acute intersections, as far as possible, 
should be avoided, and, even when they are crossed by a third line at a satisfactory 
angle, a fourth line, or an accurate rod reading from a well-determined point, is advis- 
able if within reach. 



3i6 



COAST AND GEODETIC SURVEY REPORT, 1905. 



Sometimes a position is established by measuring along the estimated direction 
from a near-by fixed point and then orienting by this assumed position and a distant 
point. This method should be used with caution, but is generally reliable for rodding 
the detail in the vicinity. 

Distortion errors.'^ — The distortion of a plane-table sheet destroys the perfect propor- 
tions which exist between the fixed points and their plotted representatives on the sheet. 

The diagram illustrates the effect distortion would have in the determination of a 
point. 



NO. 10. 




A, B, C, etc., are plotted in their true relations. After the sheet has contracted, 
a, b, c, etc., represent the relations those points have assumed. The paper contracts 
at a uniform but difFerent rate in each direction. 

The plane-table is supposed to be at X, the exact center of the figure, and it is 
required to determine the position by the distorted points a, b,c, etc. By reversing the 
telescope, we immediately ascertain that we are directly on the line HD. Reversal 
will also show that we are on the lines AE, CG, and BF. But the distortion is not 
apparent until the telescope is pointed at the signals, and the lines are drawn on the 
sheet. Then if we orient by the line HD, we shall produce the figure of the diagram, 
giving five determinations, i, 2, 3, 4, and X, each made with four well-conditioned 
points. Any one of these conditions would be considered satisfactory if we had not the 
other points to show that something was wrong. To orient by the line BF will produce 
the same result. But if we take the diagonal AE, we shall have two positions at 5 and 
7, formed by the intersection of the diagonal points, with the lines from the other points 

*See Distortion of Plane Table Sheets, Ogden, Science, Vol. XI, No. 270. 



APPENDIX 7. A PLANE TABLE MANUAL,. 317 

running wild. Using the diagonal CG would give two points at 6 and 8, with the lines 
from the other points running wild as before. 

Position by compromise. — There is no question that out of the nine positions devel- 
oped by these settings, that at X\s the only true compromise. When the sheet is dis- 
torted, all positions are compromises; and X is the true compromise in this case, for it 
is on the lines CG, AE, etc. : a below and e above, the line connecting A and E, by 
equal quantities. A line drawn through the distorted points a and e must pass through 
the middle point X. The positions 5, 6, 7, and 8 can not be true, because lines forming 
them will not pass through the opposite points when extended, which we know to be 
the condition that must be filled. 

Rules: 

(i) A station made with three points that are on the lines of contraction, the 
resecting lines forming nearly right angles at their intersection, will give the true posi- 
tion in relation to all points in the sheet (as h, b, d). 

(2) A similar condition of right-angular intersection at the station, but the lines 
forming diagonals to the lines of contraction, will give the worst possible position for 
the station (as a, c, and e). 

(3) A station made with three points on one of the lines of contraction will give 
the correct orientation of the table {a, h, and c) but not the correct position. 

(4) In estimating errors of the point due to distortion, those situated on the lines 
of contraction require no allowance, however distant. 

Application. — If the change in the sheet due to contraction or expansion gives the 
same percentage of the units of length, both lengthwise and transverse of the sheet, the 
points are still in their true relative position, and the projection is practically as good 
as when laid on the paper, but is on a slightly altered scale. When the percentage 
of change in the units of length is greater in one direction than the other, the sheet and 
projection are distorted; and to make a station by the three-point problem, the change 
of scale in each direction must be allowed for. The difficulty in making such allow- 
ances is not great, if the principal effects of distortion in the sheet are borne in mind. It 
would not be permissible, even were it practicable, to make new points on the sheet, as 
this would destroy the geographic position. It is necessary, therefore, to assume the 
new points by estimation, applying the percentage of change to the distances measured 
between the points on the lines of change — that is, on lines parallel to the edges of the 
sheet. If the point occupied and the point sighted to are on a line parallel, or nearly 
so, to one edge of the sheet, its movement from the distortion can only be along that 
line. When the position of the point sighted to is found situated to one side of the line 
parallel to the edge of the sheet, the distortion will also affect it in the direction at right 
angles to that edge, and the effect of the distortion will be most apparent when the 
angle of deflection is 45° and the position at as great a distance from the point occupied 
as the paper will permit. As the angle of deflection increases above 45° the effect 
becomes less and disappears at 90°, when the position will fall again in a line parallel 
to an edge of the sheet. 

Referring to the diagram. Illustration 10, to make a station with the three points a, 
b, c: If the sheet were not distorted, the station would be at X; A, B, and C being the true 
positions plotted when the projection was drawn. But the sheet having contracted, a, 
b, and c show the relative positions of these points; therefore we make such allowance 



3l8 COAST AND GEODETIC SURVEY REPORT, 1905. 

for the contraction derived from measuring the unit of length that we can place or 
imagine a and c to be where thej' belong, at A and C. b requires no change, as it is on 
a line parallel to the edge of the sheet. To locate A we must know the distances 
(approximately) h to a and h to X, which, multiplied by the percentages of contraction 
(in this case), will give the distance of A above and to the left of a. The same process 
locates C. ^ 

If the station were to be made with the points a, c, and e, all three points would 
have to be imagined in a new position by the same process that A has been located. 

Stations made in this way will be good for all local sketching within an area that 
the contraction of the sheet is inappreciable; but to take cuts on distant objects from 
such a station the orientation of the table must be changed. If an object is somewhere 
near the direction of a and the table at the compromise station X, the table must be 
oriented by a and X, the imaginary position A being discarded. 

The same processes apply to all positions on the sheet for the station occupied. 

Height of instrument. — Having obtained the horizontal position on the sheet of the 
occupied point, the next proceeding in the logical sequence is the determination of the 
height of the instrument above some datum plane, in order to locate and draw the con- 
tours of the area surrounding the station. The angle read and the distance between 
the occupied point and the observed point measured from the map, the height is com- 
puted by means of the tables to be found at the end of the Manual, or the result can 
be obtained mechanically by using the hypsograph. 

This instrument was designed by Assistant Fremont Morse for use in the Coast 
and Geodetic Survey and differs from the ordinary form of topographic slide-rule used 
by engineers in three particulars: First, it is circular instead of rectilinear; second, it 
does not give elevations in the same unit as the distances, but gives heights in feet 
when the distances are measured in meters; and third, the arguments used for deter- 
mining the heights are the horizontal distance and angle of elevation instead of inclined 
distance and angle of elevation. 

The instrument will indicate the difference of height (uncorrected for curvature 
and refraction) for any distances and angles encountered in ordinary topographic work, 
with an error much smaller than the probable error of observation of the plane-table 
alidade. 

For complete description and directions for use, see Appendix 4, Report for 1902. 

Relief. — There are two methods of representing it^ — by hill shading and b}^ contours. 

Hill shading is generally effected b}^ a system of lines, called hachures, drawn in 
the direction of the slope. When it is steep, the hachures are thick and closely spaced. 
On the other hand, a gentle incline will be indicated by fine lines widely separated: 

Conto2irs * or horizontal curves are the outlines of horizonal sections of ground at 
different elevations with designated equal intervals between their planes, delineated in 
their true positions relatively to each other and to the rest of the map, and conforming 
to the scale of the map itself; or, briefl}^ a contour is a curve produced by the intersec- 
tion of the horizontal plane with the surface of the ground. They may also be described 

*For interesting articles on the diagrammatic properties of the contour line see: On Contour and 
Slope Ivines, Cayley, London & Ed. Mag., 1859, pp. 264-268; On Hills and Dales, Clerk Maxwell, 
ibid, 1870, pp. 421-426; Properties of Matter, Tait, 1890, pp. 70-81. 



NO. 11. 




o9 



y^nirirlA-AM^v''^' ^ 



•e. 



HYPSOQRAPH. 




-K 





51D£ VIEW 



TOP VIEW 




SECTION 



HYPSOGRAPH. 



NO. 13. 



DiagrajTL ilhistTxttiruj the mode of corxstructing Profile from. FUxn. 




No. 14: 




Crest, Face, and Talus of a Granite Cliff {Eagle Cliff, Mt. Desert Id.) 




<O0 

p 







APPENDIX 7. A PLANE TABLE MANUAL. 319 

as imaginary shore lines formed at stated or regular elevations, by water which is sup- 
posed to rise successively to these elevations over the face of the country. 

Profile. — As each curve has equal vertical ordinates at all points, the elevation or 
profile of a hill, as well as a model in relief, can be constructed from the map, when it 
is accurately executed on a large scale, without further field measurements. 

A profile of a hill is the outline or trace formed with its surface by a vertical plane 
cutting the hill in any direction. 

Illustration No. 13 shows the profile through the line A' B' oi the hill h, as repre- 
sented on a topographic map. The full parallel lines upon the profile represent the 
successive heights or sections of the hill of 20 feet, and the broken or intermediate lines 
XXX those of 10 feet. A reference to the letters of the diagram is all that is 
necessary to a full understanding of the subject: a is the shore line or high-water line 
upon the map, x x x are the auxiliary lo-foot curves; f the coincidence of curves 
upon the chart at the perpendicular face of the hill f, upon the section. This is the 
only case where contours of different heights run into each other upon a topographic 
plan. D' is a depression in the face of the hill, represented on the profile by D. d' is 
a barranca or dry broken gully, and c' c' a water course. 

It will be plain that if we were to suppose the water to rise to a height of 20 feet 
above the high-water line, to h on the profile, the 20-foot curve upon the map would 
become the shore line and the depression D' would fill up and become a pond of water; 
and if the water were to rise to a height of 30 feet, the dotted broken line would form 
a shore line, and the knoll G would become an island. 

Advantages and disadvajitages of hill shading and contours. — In a mountainous 
country the method of hill shading presents a picture which expresses more forcibly to 
the eye the configuration of the country than a system of contours. But the objection 
to its sole use arises from the fact that, although one ridge is perceived to be higher 
than another, there is no guide for stating in terms of some linear unit this difference 
in elevation. It also obscures the symbols representing other details on the surface. 

A system of contours furnishes a convenient means for obtaining the heights on 
any part of a map, but does not adapt itself to the representation of the small but 
important accidents of the ground, such as gullies, ledges, rocks, etc.; nor does it 
satisfactorily delineate such features as cliffs, bluffs, quarries, railroad cuts, and 
embankments. 

For these reasons the Coast and Geodetic Survey has adopted both methods, 
employing hachures for the smaller features and where the steepness of the slope would 
make the contour lines approach together so closely that individual lines would become 
indistinguishable, and relying on the contours to delineate less precipitous ground. 

The two systems can be seen combined when it is necessary to indicate a rocky and 
broken mountain face. (Illustrations 14 and 15.) 

The contour interval customarily used on the Coast and Geodetic Survey field sheets 
is 20 feet. When, however, the contour runs very near to some remarkable accident 
of ground, as a prominent spur or indentation, a slight deviation above or below its true 
plane is admissible to include this feature, although it is preferable to avoid doing so, if 
possible, by the introduction of an auxiliary curve. 

In abruptly mountainous and comparatively inaccessible regions, where sketching 
must be relied upon, 100-foot curves may suffice to develop all necessary features. 

' 38077°— 16 3 



320 COAST AND GEODETIC SURVEY REPORT, 1905. 

Datum plane. — Probably the best plane of reference for heights of points on the 
earth's surface is the mean level of the sea, since the mean of the rise and fall of the 
tides is approximately this level. In practice, however, mean high water is usually 
taken, as it includes all land not covered by the tide range, and is the line dividing 
land and water. ^ 

Reference signal. — It is advisable in commencing the survey of a region bordering 
on tide water to locate one or more signals at the assumed high-water line, carefully 
noting the height of the top of the flag above the same, to be used in measuring angles 
of depression for heights from points occupied during the progress of the graphic trian- 
gulation. As the heights of other points are determined in the course of the survey and 
verified from observations from two or three other points, these in turn may be used for 
the same purpose. 

The following are the methods of surveying curves of equal elevation : 

First. The determination of the position and heights of a number of characteristic 
points of the terrene, and with these as guides tracing the contour lines. 

This is the method generally used in surveys embracing such areas as the sheets of 
the Coast and Geodetic Survey on scales of i-ioooo and 1-20000. 

It has the merit that the development of the terrene proceeds with the survey of 
the skeleton, and does not necessitate a return to a station when once occupied. In 
connection with the determination of position by resection it works harmoniously and 
economically, since points that would be selected for position as having the best outlook 
are likely to be the characteristic ones of the terrene. 

Second. Surveying and leveling the skeleton and its traverses. 

Third. Surveying and leveling the profile lines. 

The profile is a traverse line on which are determined the heights of the points at 
which the surface changes slope. The points where this line is intersected by the suc- 
cessive contour interval are easil}^ determinable with the level and rod. 

Fourth. Surveying and leveling the base of each level section. 

To determine the base of each level section the table is set up in position where this 
level intersects the profile, and using the alidade as a leveling instrument, with a target 
fixed on the rod at the height of the optical axis of the telescope, the line is traced by 
locating the rod in successive positions at characteristic points of the terrene, when the 
target comes in the horizontal plane of the optical axis, direction and distance of the 
rod being determined and drawn in each case. A line drawn through these points, 
recognizing features between the stations, locates the curve. In this operation allow- 
ance should be made for curvature and refraction, when the distance becomes sufficiently 
great to make it a factor. 

Fifth. Surveying and leveling the parts of several level sections from one station. 

When parts of several level sections are run from one station, set up the table at a 
point on a contour, and observe on a staff the height of the optical axis of the alidade. 
Set a target on the staff above this height as many contour intervals as its length will 
include. The aid carries the staff below the instrument and is signaled to stop when 
the target comes in the horizontal plane of the optical axis, and at successive steps 
traverses the lower curve. The target is then lowered on the staff one contour interval 
and the next curve above is traced in the same manner, continuing the proceeding until 
the level of the instrument is reached, when the table is moved to an upper station 



NO. 16. 




TYPICAL CONTOUR GROUPS. 



APPENDIX 7. A PLANE TABLE MANUAL. 32 1 

and the proceeding continued until the summit is reached. (Applies only to very small 
contour intervals. ) 

Sixth. The division of the terrene into squares, triangles, or parallelograms. 

By the mode of regular division of the surface into squares, triangles, or parallelo- 
grams, pegs are driven at regular intervals, and their heights determined by level in the 
way that may be most convenient, a spirit-leveling instrument being the most accurate. 

Station routme. — The topographer having determined his position on the sheet, 
and also the height of the instrument, proceeds to map the natural and artificial details 
of the area surrounding the station. For this purpose the direction of each detail is 
obtained bj^ pointing the telescope upon it, the edge of the rule cutting the station 
point; its distance is determined by reading the stadia rod held there for the purpose. 
This distance is then taken off the metal scale with a pair of dividers and plotted 
along the edge of the rule. 

While this is in progress the alidade is used both as a level for the observation of 
objects of the same height as the instrument and for measuring angles of elevation and 
depression to such of the plotted details whose position at critical points of the contours 
would materially assist the topographer in tracing them. 

Number of elevations to be determined. — No rule can be laid down as to the number 
of elevations that should be determined from each plane-table station or for a given 
area. It will depend on the skill of the topographer and the modeling of the ground. 
The number will be adequate when he is confident of tracing, by their aid, the contours 
with an accuracj^ sufficient for the scale and the purpose of the survey. 

It would indicate careless and slovenly work if the contours were found on exam- 
ination to deviate frequently from their true position on the sheet by more than half an 
interval for a slope of less than 5° in an open country. When the slope is steeper, or 
in wooded regions, a greater latitude is permissible, but even here, in representing the 
crests of ridges, prominent hill tops, and valley floors, this limit of half an interval should 
not be departed from for good work.* 

Contour sketching. — The topographer will be assisted in sketching contours, where 
the modeling is intricate, by lightly drawing a skeleton composed of the ridge lines and 
thalweg lines (lowest lines of valleys) in their proper positions around the station. On 
the ridge lines will be found the extreme outward or convex bends of the contours, and 
on the thalweg lines the extreme inward or concave bends. 

It can be readily imagined that if each spur and each small depression was repre- 
sented by its appropriate line, and on each of them were located, either by observation 
or estimation, points having elevations equal to some multiple of the contour interval, 
it would be only necessary to connect those points having the same elevation with a 
smooth curve to have a correct plan of the contours. 

It will simplify the sketching at a station to draw the highest, lowest, and middle 
contours first, as they will then serve as guides for estimating the position of the others. 

Typical contour groups (Illustration 16). — It should be remembered that a con- 
tour never splits, as shown in Fig. i; nor do two contours run into one, as shown in 

* For some pertinent remarks on this subject see Bulletin of the University of Wisconsin, Eng. 
Series, Vol. i. No. 10, Topographical Surveys; their methods and values. J. F. Van Ornum, pp. 
360-361. 



322 COAST AND GEODETIC SURVEY REPORT, 1905. 

Fig. 2 ; nor cross each other, except in the rare instance of an overhanging cliff, as 
shown in Fig 3. 

When an auxiHary contour is introduced, no more of it is drawn than is sufficient 
to deUneate the special feature which makes it necessary. A principal contour, on the 
other hand, can not have an end within the map; if it commences at one edgexit must 
terminate at another. 

A closed contour encircled by one or more closed contours is either a hill, as shown 
in Fig. 5, or a depression, as shown in Fig. 6; the arrows showing the direction in 
which water would run. The summits of all the hills of importance should have their 
elevations determined and marked on the map. All depressions without an outlet and 
which do not contain a pond or lake should be marked with a D at their lowest point. 

A series of contours, as shown in Fig 4, is either a croupe (the end of a ridge or 
promontory) or a valley. If a croupe, the contours will have their concave sides 
toward the higher ground; if a valley, the contours will have their concave sides toward 
the lower ground. 

A combination of four sets, like Fig. 7, with convex sides turned toward each other, 
represents a dip in a ridge, or the junction of two ridges, and is called a saddle. 

A pass in a mountain range generally takes the form shown in Fig. 8. 

Order of development of contoiirs. — As the progress of topographic work is usually 
from the shore line inward, this affords the most favorable direction for drawing the 
curves of equal elevation, and as it is desirable that all work at a station shall be com- 
pleted when it is first occupied to avoid the necessity of returning to it, the curves should 
be drawn by estimation from the shore line to the points sighted and determined for 
position and height, to be checked by drawing from those points when in turn occupied. 
The heights of a sufficient number of points must be determined to guard against any 
wide range of estimate of height by the eye. 

In abrupt slopes of considerable extent the use of a pocket clinometer is valuable 
in determining the degree of slope, and in order to draw the curves by the widths of 
their zones (the cosines of angles of slope) from a paper scale prepared for the purpose. 
(See Illustration 32.) 

Filling in. — Having completed the work at a given station, the topographer proceeds 
with his party and instruments to an adjoining locality, where he selects a new station 
from which he can gather the details of an area bordering upon the one last surveyed. 
In this manner the skeleton map is filled in by successively occupying stations over the 
whole expanse of the sheet. 

Traverse lines. — -In a wooded country, where it is impossible to find open space with 
range suificient to see enough points for determination of position by resection, it is 
necessary to run traverses along the roads, with offsets to such lateral features as it 
may be practicable to reach without the expenditure of excessive labor and time in 
opening lines of sight. The levels, when necessary, are carried along with the line by 
observing vertical angles with the alidade upon some mark on the rod, taking back and 
fore sights at alternate stations. 

Mai7i traverse. — The standard table is used on main roads and whenever the details 
are important and numerous. 

The traverse line is started by occupying some point previously determined and 
sending the telemeter rod ahead to a place selected for its advantageous position, in 



APPENDIX 7. A PLANE TABLE MANUAL. 323 

reference either to the surrounding features or facility in obtaining a new section of 
the traverse. 

Having sighted to this point, read and plotted the distance, short guide lines .should 
be drawn along the edge of the ruler at both ends and numbered or lettered, so they 
may be identified from others of like character. The table is then moved to the forward 
station, approximately oriented by estimation, and the plotted point carefully plumbed 
over the one on the ground. 

The alidade is now placed on the table, and the table oriented by bringing the edge 
of the ruler close up to the guide lines; then revolving the table until the vertical wire 
bisects the rod or signal left for that purpose at the last station. 

The same processes which were employed at the initial station are now repeated; 
the detail is mapped and the new station in advance occupied in turn, the line progress- 
ing in this manner by successive steps. 

In running traverses, great care should be taken to sight as low as possible upon 
the fore and back signals, so as to avoid any error of deflection which might arise from 
the inclination of the signal poles. 

Stibordinate traverse. — When the line is unimportant and few features present 
themselves to be noted, an auxiliary plane table oriented by a declinatoire or a transit, 
fitted with stadia wires, may be employed. 

When this method is pursued with a second table the forward rod station is not 
occupied, but another is chosen in advance of it, from which it can be seen where the 
instrument is set up and oriented with the declinatoire. Sighting the alidade to what 
is now the back station, the distance is read and plotted along the edge of the ruler, 
and the point so determined represents the one occupied by the table. 

The pivot on which the declinatoire needle rests should be examined frequently 
as the least roughness will cause the needle to drag and introduces serious deflections 
in azimuth. 

All traverse lines should start and end at well-determined points. This will serve 
to check the accuracy of the work. If the closing error is not too large, the line should 
be adjusted by distributing it throughout its length. The line is run on a spare sheet 
when an auxiliary table is used; then traced, "swung in," and adjusted between the 
two fixed points. 

Determinations for hydrography. — Where the topography surveyed includes the 
shore line of a body of water, the hydrographic survey of which is intended to follow the 
topographic work, as in the Coast and Geodetic Survey, it is the duty of the topographer 
to locate and determine the shore signals, and it is only necessary to state that they should 
be so placed as to furnish the hydrographic party with as many points as is desirable for 
the determination of positions on the water. 

Natural or artificial objects along the shore, or in plain sight from the water, such 
as fence ends, rocks, prominent houses, etc. , should be determined and marked upon 
the sheet. 

lyines to buoys and other permanent floating objects at anchor should be, as far as 
practicable, taken at the same stage of the tide, or direction of current. 

The mean low-water mark should be delineated, and when it is beyond the reach of 
the plane-table and presents no marked points for determination, or is of a character 
that will not permit the use of the instrument — as along the swampy shores in the 



324 COAST AND GEODETIC SURVEY REPORT, 1905. 

South, where the muddy shoals extend far seaward, and among the shifting quicksands 
of our great estuaries and bays — it may be left to be traced by the work of the hydro- 
graphic parties. The channels through mud flats of this character should be indicated, 
however, if only approximately, by cuts and tangents, or the determination of stakes 
at the turning points. Where the fall of the tide exposes rocks and ledges, shingle 
beaches, etc. , their character and extent should be delineated and distinguished from 
the sandy beaches, as these features are most difficult and laborious for the hydro- 
graphic survey to represent. 

High-water and storm-water line. — In tracing the shore line on an exposed sandy, 
coast care should be taken to discriminate between the average high- water line and the 
storm- water line. 

Determination of inaccessible points. — On a precipitous coast, where the shore line is 
inaccessible and can not be determined by ordinary methods, the salient features are 
located, when occupying commanding stations, by observing the vertical angles upon 
them, and drawing direction lines to them. Then using the elevation of each station 
as a base the distance to each feature is computed and platted. 

The same method applies to outlying rocks, and is often employed where there is 
any doubt of their being identified from different places. 

Large-scale surveys. — As has been previously stated, i-ioooo and 1-20000 are the 
scales customarily used in the execution of the topographic work of the Coast and Geo- 
detic Survey, as they are the ones best suited for the charting of the coast line and 
harbors of the United States. 

Other surveys for special purposes have been made from time to time on scales 
both larger and smaller, and the field practice has been modified according to the require- 
ments of the scale used. 

A topographic survey of the District of Columbia outside the thickly populated 
limits of the city of Washington was made between the years of 1880 and 1891 on a 
scale of 1-4800. 

The methods pursued are here described, as they are typical of other surveys on a 
large scale. 

Based on a sufficiently minute triangulation, the plane-table and stadia, wye level, 
and rod were used for all determinations of details. The relief was elaborately indicated 
by contour intervals of 5 feet. The datum plane is the same as used by the engineer 
department of the District, on which is based all the levels used for grades of streets and 
sewers in the city of Washington, the survey being made for the purpose of extending 
streets and avenues beyond the city limits. 

From this datum, along all roads, avenues, and railroads, and where roads were 
infrequent, across country, lines of level were run, and after careful checking in the 
usual manner bench marks were placed in position convenient to all parts of the region. 

The plane-table stations were established so as to easily overlook every part of the 
field and so close together that each was surrounded by the others within the range of 
a single reading of the stadia rod. 

The mode of procedure was as follows: 

The plane-table was placed in position by a graphic solution of three-point 
problem. At the same time the height of the level was determined above some near 
bench mark and the target of the level rod fixed, so that when it was in the line of sight 



APPENDIX 7. A PLANE TABLE MANUAL. 325 

of the level the bottom of the rod would rest on the ground where the elevation corre- 
sponded to that of some contour. The level rodsman then began his journey along this 
imaginary horizontal line, holding the rod for the observation of the levelman at each 
noticeable change in the configuration of the ground. The levelman directed the rods- 
man by signals at each point until the rod was in position on the contour line, when the 
stadia rod was substituted and its distance read and plotted on the plane-table sheet. 
The rodmen followed the contour line in both directions from the table as far as the 
stadia rod could be conveniently read. Geneifally two and sometimes three contours 
were run from one level station, and on their completion a turning point was fixed and 
the level shifted to higher or lower ground, as the circumstances required. 

A survey of Craney Island, Virginia, was made in the same manner on a scale of 
r-i2oo. 

RAPID SURVEYS. 

Military reconnaissance. — In almost every field of operations, from the commence- 
ment of the civil war to its close, the plane-table was used. 

Until this time very little was known, save in theory, of the value of the plane-table 
as a reconnoitering instrument, and all the officers engaged in the work testify that, for 
rapidity and accuracy in the execution of military reconnaissance, it is more effective 
than any other instrument. 

The system usually adopted, in default of triangulation , was to measure a base 
with an ordinary chain and to do triangulation with the plane-table. 

In detailed surveys for the Army, where a topographer averages from i to 3 square 
miles a day, on large scales a chained base of from one-half to three-quarters of a mile 
for the survey of an area of 25 square miles is found sufficient. 

At Chattanooga, from two different bases of about half a mile each, plotted on 
separate sheets, and carefully measured once with a common 20-meter chain, the 
same chain being used to measure both bases, after considerable intermediate plane- 
table triangulation carried on by two officers, two objects were determined 2^ miles 
apart, common to both sheets, which were on a scale of i-ioooo, and the discrepancy 
was but about 15 meters. Many other points of junction indicated this to be the maxi- 
mum error. In this case the leaves were mostly off the trees and the hills afforded 
good points. The sheets covered about 20 square miles each. At Nashville there 
was a discrepancy of about 10 meters in 2 miles. 

At other times, when the character of the country or the pressure of time did not 
admit of the measurement of a preliminary base and plane-table triangulation, the 
work was commenced by starting from a single point and extended by linear measure- 
ment with the chain or stadia, intersections from the ends of the chained lines being 
taken to determine objects, which, as the work progressed, could also be used as checks 
upon the chaining. Where circumstances permitted, an occasional return with the 
chain to a back point, either to close a series of lines upon it or to start afresh, was 
resorted to. This work was generally carried on over roads and the interior filled in by 
sketching and intersections as far as practicable. Some of the tests of this latter work, 
where the operations of two officers joined, were remarkably close. 

A very efficient topographic officer estimates that with the usual number of hands 
and a good sketcher to aid, in a country of average variety of detail, in which all the 



326 COAST AND GEODETIC SURVEY REPORT, 1905. 

houses, prominent barns and outbuildings, streams, roads, general outline of woods, and 
approximate curves are to be shown, on a scale of i-ioooo, an area of between 2 and 3 
square miles can be filled in daily, with sufficient accuracy for military purposes. 

This rapidity of work, however, could not be expected in or near towns or populous 
districts. It is doubtful if, under average conditions, the work would be more than one- 
half this amount. 

In some thickly wooded sections and where time is limited, it has been found 
advisable to run the main roads with the' plane table and fill in with the compass, which 
is more rapid but less accurate than where the entire work is done with the plane table 
alone. The usual method employed where these methods were combined, was as follows: 
Where the army was stationary, or moving leisurely, one main road was run with the 
plane table, the operator being accompanied by assistants well practiced in the use of 
the compass. Upon arriving at any important road or water course an assistant was 
sent to the right and left, starting from a plane-table point, determined by the chaining, 
and running as far as was requisite and then returning to the main road again to repeat 
the operation, the compass notes, of course, being kept in a book prepared for the pur- 
pose. Prominent points determined by the plane table were used as checks in the 
compass work. The intervening topography, where no compass or plane-table work 
had been done, was sketched in by the chief of the party, in which accurate pacing 
became of great value. 

Wii/i compass and notebook. — Plane-table methods can be utilized to advantage 
when compass, pencil, notebook, and ruler are the substitutes for an instrumental outfit. 
The book serves as the sheet and board combined, and the ruler, as it was in the early 
days of the art, becomes the alidade.* 

Photogrammetry .\ — In the topographic reconnaissance made for the Alaska Bound- 
ary Survey by the Coast and Geodetic Survey, the camera with constant focal length 
has been used as an adjunct to the small mountain plane table. The latter was 
used to plot the shore line and adjacent topography, also to determine as many peaks 
of the interior country as possible by the intersection of lines of direction. All camera 
stations were determined geographically and hypsometrically, and plotted upon the 
plane-table sheet. The topographic details beyond the reach of the plane-table were 
added to the map in the Office by the photogrammetric methods. 

The rugged mountains of southeast Alaska appear particularly well adapted for 
this mode of procedure, as identical points can be readily picked out from different pan- 
orama views, owing to the characteristic shapes of the mountain peaks, snow fields, 
glaciers, etc. 

Periods of fair weather are also very short and of rare occurrence in that locality, 
and a great deal of topographic material can be gathered photographically in a short 
time, which when plotted will cover a large territory if a sufficient number of reference 
points on the views have been located instrumentally. 

The plotting proper can be carried out to any degree of minuteness and detail; the 
only requirement is that a sufficient number of camera stations shall have been occupied 

*See "Sketching without instruments," in Topography, Drawing, and Sketching, by Lieut. Henry 
A. Reed, U. S. Army, 1886. 

fSee United States Coast and Geodetic Survey Report, 1893, Appendix 3, and Report for 1897^ 
Appendix 10. 



APPENDIX 7. A PLANE TABLE MANUAL. 337 

to fully cover the territory in question, so that every topographic feature of prominence 
has been seen or photographed from at least two stations. ■ 

By this application of photogrammetry the plane-table methods of determining 
topographic details are extended to the Office, inasmuch as the same features are 
selected from the panorama views and plotted geographically which would have been 
located by the plane-table. But the actual time spent in the field is reduced at the 
expense of the time needed for office work. 

Survey in advance of triangulation. — Where it is necessary to make a topographic 
survey in advance of the determination of points by triangulation, a reconnaissance is 
first made for the location of a base line and selection of points to be determined with 
the plane table. 

The base is measured with sufficient accuracy and conveniently, with a steel tape 
which has been compared with a standard at a fixed tension, and to one end of which is 
attached a spring balance to secure the same tension during measurement. The suc- 
cessive lengths are marked by lines cut on copper tacks driven in wooden stubs firmly 
set in the ground. The temperature is noted at frequent intervals as the work progresses, 
and the corrections are applied to the length of the base when completed. 

The base is then properly located on the sheet in reference to the area to be 
embraced and its length carefully set off. It is well at the same time to mark in three 
or four different parts of the sheet lengths of i 000 meters for the purpose of determin- 
ing at any time the true scale of the sheet, variable by the different hygrometric condi- 
tions of the atmosphere. 

Signals having been erected at the selected points, the extremes of the base are 
occupied with the table and the 'points, as far as may be reached with good intersections, 
determined from them and lines of direction drawn to all the points visible, to serve as 
checks upon their determination from other points furnishing directions for good inter- 
sections. The survey then proceeds as usual. 

It is well at the beginning of work to draw (using the declinatoire) the magnetic 
meridian, at some determined point near the middle of the sheet for the purpose of put- 
ting the table in approximate position at any station with the declinatoire. The manner 
of doing this is described elsewhere. 

Before finishing the field work it is important, when the sheet has no projection, to 
provide data for drawing a true north and south line. This is done by drawing from 
a point upon the sheet, when the table is in position, a line in the vertical plane through 
Polaris and the point occupied and recording the time of observation. The azimuth of 
the star at that time being known, a true north and south line can accordingly be set off. 

If a small transit instrument is at hand and carefully adjusted for movement in 
vertical plane, an assistant with a lantern can be located where the vertical plane through 
Polaris and the point occupied intersects the ground, at as great a distance from the 
point as the ground will admit within the limit of communication by light signals. 
When such a position is marked the direction from the point occupied may be deter- 
mined by daylight. 

If, in the absence of a transit, the alidade has not vertical range sufficient to observe 
Polaris, an illuminated plumb line may be used for the alignment. 



328 COAST AND GEODETIC SURVEY REPORT, 1905. 

OFFICE WORK. 

All the topographic features of a survey should be drawn in pencil upon the sheet 
in the field, while they can be seen. Sketching and plotting in the office from notes, 
unless the country be near at hand for ready reference in case of doubt or defective data, 
is objectionable. When this is unavoidable, the sketches should be transferred to the 
sheet as soon as possible after being made, while fresh in the mind of the person by whom 
they were made, and by whom they should be plotted. Days which, from inclemency 
of the weather, are unfavorable for out-of-door work should be allotted to this purpose, 
and advantage should be taken of them, also, for retouching any details of the sheet 
which may have become indistinct, as it is very important that they should not be left 
indefinite or become obliterated; for when the inking is done, as it generally is, at a 
distance from the field of operations, the necessity for this care is obvious. Nos. 4 
and 5 pencils are good for this purpose, for which very hard or very soft and black 
pencils are equally unsuited. 

In the inking of a topographic sheet three requisites to its proper appearance 
when finished should be borne in mind — clearness, neatness, and uniformity. 

The lines and objects should be clear and sharply defined, nothing being left obscure 
or doubtful; the paper should be kept unsoiled, and erasures avoided as far as possible, 
and the style and strength of the drawing should be the same throughout. It is an 
important matter that an easy and natural appearance should be given to the sheet, for, as 
before remarked, a mere rigid adherence to conventional signs is not all that is neces- 
sary; while there should be no deviation in this respect, at the same time the drafts- 
man should strive to represent the country. There is a great difference with regard to 
this among topographers. Two correct sheets of the same section of ground, executed 
by different persons, may be inked, and while one will have a stiff and ungraceful look, 
the other will appear artistic and natural, giving at once the impression of a true repre- 
sentation of the country surveyed. 

Office work should not be commenced until the topography is entirely completed, as 
no inked or partially inked sheet should ever be used in the field. Sometimes, for the 
special examination of old work, or for the insertion of some recent artificial or natural 
changes, this becomes necessary, but there is always a risk of injuring an inked sheet 
by exposure to the weather or by using it upon a plane table. 

The inking should begin Vi'ith the high and low water lines. The high-water line 
or shore line proper should, in all cases, be full and black, the heaviest line on the 
sheet, and in this, as in all the rest of the ink work, the lines of the surveyor should 
be strictly adhered to. 

The topography as drawn in the field is supposed to be correct when the sheet is 
finished, and no ofiice amendments or changes are admissible. The low-water line is 
drawn, not so full as the former, but clear, black, and uniform, consisting of a dotted 
line for sand and mud and the conventional sign where it is formed by shells, rocks, 
or coral reefs. 

Neither the inner border of a marsh nor a shoal covered at high tide has a distinct 
continuous line to mark its limits, each being represented in its proper form and within 
its area by its conventional sign only, but the shape should be well and correctly 



APPENDIX 7. A PLANE TABLE MANUAL. 329 

defined. All objects between high and low water, covered at full tide, should be repre- 
sented less boldly than the other features on the sheet, but not faintly or indefinitely. 

The roads should be inked plainly and evenly, with their sides parallel, except 
where the survey shows a deviation from the general width. Main thoroughfares when 
fenced are drawn with a full line, subordinate roads where fenced should be shown by 
the usual sign, and where there is ro inclosure a line of dashes should indicate the road- 
side, and then should follow the fences and houses. In drawing the latter, care must 
be taken that the corners and angles exhibit a sharp, clear outline, which adds much to 
the appearance of the sheet. 

The general skeleton of the survey being now completed, the contours are drawn 
with a bold, uniform, plain red line, without break, over all the other work, following 
accurately the full range of level of each of the contours on the sheet. 

After this comes the general filling in, by conventional signs, of sand, marsh, grass, 
cultivation, orchards, rocks, hachures, etc. Some practice is needed to execute the sand 
work regularly and neatly. It should never be done hurriedly, though of course 
rapidity in this respect follows practice. The lines representing marsh, and the delin- 
eation of grass on the fast ground, should always run in the same direction over the 
whole sheet and be parallel to the top of the sheet and the title. The appended draw- 
ings (Illustrations 17, 18, 19, 20, and 21) give the conventional signs as adopted by and 
now used by the Coast and Geodetic Survey. 

The most difficult part of the inking for a beginner is the lettering, which now 
follows, and for which samples are given (Illustration 22). It is expected that every 
topographer shall have learned to draw sufiiciently well to ink his sheet in a clear and 
distinct manner and letter it with some regard to neatness and graphic effect, as the 
appearance of an otherwise well-inked sheet is marred by careless or indifferent lettering. 

The location of the names upon the sheet should be such as not to cover or oblit- 
erate any detail or feature of the survey, and the letters should be put on neatly and 
gracefully, and in point of size and form according to the specimens furnished. The 
title should follow, with such notes as may be necessary to explain any peculiarity 
of .the sheet or survey.* This title and lettering should, as far as practicable, be so 
placed that when the sheet is held with the top (the north end of the map) from you 
it can be easily read; in other words, as nearly parallel to the top or upper end of the 
sheet as the nature of the work will admit. All names well established and recognized 
in a neighborhood, both general and local, should be collected during the survey, and 
their correct orthography ascertained, and in case of any doubtful or disputed orthog- 
raphy a report should be made giving an}' traditions or authorities which bear upon 
the subject. No illuminated or German text, old English, or what is known as "fancy 
printing," should be indulged in, a strict adherence to simplicity being required. 

The minutes of the parallels of latitude and meridians of longitude should be 
marked in figures at the upper and right-hand ends, respectively, the degrees on the 
center parallel and center meridian only. 

When buoys are determined by the topographer, and their names, colors, numbers, 
or kind are known, they should be placed on the sheet and so marked. 

* The topographers in the Coast and Geodetic Survey are required to write the title and notes on 
a separate sheet of paper and attach it to the plane table sheet. This portion of the lettering is done 
at the Office. 



330 



COAST AND GEODETIC SURVEY REPORT, 1905. 



The triangulation points should be surrounded by a small red triangle. Barns, 
houses, prominent trees, and other objects determined by the plane table that may be 
used as points of reference in making additions to the sheet subsequent to the survey 
should be indicated by a small blue circle. 



TABLES AND FORMULA. 



Table for reducing readings of inclined sights on a rod held perpendicular to the line of sight. 



Angle 


Hypothenuse 














100 meters 


200 meters 


300 meters 


400 meters 


500 meters 


5° 


99.62 


199. 24 


298. 86 


398. 48 


498. 10 


10° 


98.48 


196. 96 


295- 44 


393- 92 


492. 40 


15° 


96.59 


193- 19 


289. 78 


386. 37 


482.96 


20° 


93-97 


187. 94 


281.91 


375-88 


469. 85 


25° 


90.63 


181.26 


271. 89 


362. 52 


453- 15 


30° 


86.60 


173. 21 


259. 81 


346. 41 


433- 01 


35° 


81.92 


163. 83 


245- 75 


327- 66 


409. 58 


40° 


76. 60 


153- 21 


229. 81 


306. 42 


383. 02 


45° 


70.71 


141.42 


212. 13 


282. 84 


353- 55 



When it is desired to use the preceding table, a sight must be attached to the rod or 
the proper position of the rod left to the judgment of the rodsman. The usual and 
safer way is to have the rod held vertical for all readings. There are then two corrections 
to be applied, one to reduce the inclined distance to a horizontal one and one for the 
oblique view of the rod. 

The equation for reducing the readings is: 

Horizontal distance=r cos^ z^+(<^+y^) cos v 

Where r= reading of vertical rod; 

z'^ angle of elevation or depression; 
r= distance of object glass to center of instrument; 
y= focal length of telescope. 
The following table gives the coefficient of reduction by which the rod reading is 
to be multiplied. It is based on the assumption that c-\-f\s to be added to the result to 
obtain the distance to the center of the instrument. 

Example: Given an angle of elevation or depression 8° 10' and the reading of the 
inclined sight on vertical rod=i73.i meters. 
From the table: 

Factor for i meter for 8° \o' multiplied by 100=97. 98 meters. 

" 7 " " " " " " 10=68.59 " 

" 3 " " " " = 2.94 " 

" " 0.1 " " " " = .09 " 

Horizontal distance 169. 60 " 

To which c-Vf\s, to be added. 



APPENDIX 7. A PLANE TABLE MANUAL. 



331 



Table of coefficients for reducing readings of incliiied sights on a vertical rod to horizoyital 

distance.'^ 




♦Computed by J. A. Flemer, Assistant, Coast and Geodetic Survey. 



332 



COAST AND GEODETIC SURVEY REPORT, 1905. 



Table of coefficients for reducing readitigs of inclined sights on a vertical rod to horizontal 

distance — Continued. 



Angle of 
inclina- 
tion 








Horizontal projection of 


\ 


I m. 


2 ni. 


3 m- 


4 m. 


5 m- 


6 m. 


7 m. 


8 m, 


9 m. 


3C/ 
40' 
50' 


• 98444 
•98371 
. 98296 
. 98220 
. 98142 


1.96888 
1.96742 
I. 96592 
I. 96441 
I. 96285 


2. 95331 
2. 95II2 
2. 94889 
2.94661 
2. 94427 


3- 93775 
3-93483 
3-93185 
3. 92881 
3-92570 


4.92218 

4- 91854 
4. 9I48I 
4. 9IIOI 

4.90712 


5. 90662 
5.90225 

5- 89777 
5- 89322 
5- 88855 


6. 89105 
6. 88596 
6. 88073 
6. 87542 
6. 86997 


7- 87549 

7. 86967 

7- 86370 
7- 85762 
7. 85140 


8- 85993 
8-85337 
8. 84667 
8.83982 
8. 83282 


8° 00^ 


. 98063 


I. 96126 


2.94189 


3- 92252 


4- 90315 


5- 88378 


6. 86441 


7. 84504 


8. 82568 


10^ 
20' 
3C/ 
40' 
50' 


• 97982 

• 97899 

• 97815 
.97729 

• 97642 


1.95964 
I- 95798 
I- 95630 

1-95459 
I. 95284 


2. 93946 
2. 93698 
2-93446 
2. 93188 
2. 92926 


3.91928 
3- 91598 
3-91261 
3. 90918 
3- 90568 


4. 89910 

4- 89497 
4. 89076 
4. 88647 
4. 88209 


5. 87892 
5- 87396 
5. 86891 
5- 86377 
5-85851 


6. 85874 
6. 85296 
6 . 84707 
6. 84106 
6. 83493 


7- 83856 
7.83196 
7. 82522 
7. 81836 
7.81134 


8. 81839 
8. 81096 
8. 80337 
8. 79565 
8. 78777 


9° 00' 


• 97553 


I. 95106 


2. 92658 


3. 902 1 1 


4- 87764 


5-85317 


6. 82870 


7.80423 


8. 77975 


10' 
20'' 
30^ 
40' 
50' 


• 97462 

• 97370 

• 97276 
.97180 
.97083 


I. 94924 
1.94740 
1-94552 
I. 94361 
I. 94166 


2. 92386 
2. 921 10 
2. 91828 
2. 91542 
2. 91250 


3- 89848 
3- 89480 
3- 89104 
3.88722 
3- 88333 


4.87310 
4. 86849 
4- 86379 
4. 85902 
4- 85416 


5- 84772 
5- 84219 
5. 83655 
5- 83083 
5. 82499 


6.82234 
6. 81589 
6. 80931 
6. 80263 
(>■ 79583 


7- 79696 
7- 78959 
7- 78207 
7- 77444 
7. 76667 


8. 77159 
8. 76328 

8. 75483 
8. 74624 
8. 73750 


10° 00' 


• 96985 


1.93970 


2. 90954 


3- 87938 


4- 84923 


5-81907 


6.78892 


7. 75876 


8. 72861 


10' 
20' 
30' 
40' 
50' 


. 96884 
. 96782 

• 96679 

• 96574 
■ 96467 


1.93769 
I- 93565 
1-93358 
I. 93148 
I. 92934 


2- 90653 
2. 90347 

2. 90037 
2. 89721 
2. 89402 


3-87537 
3.87129 
3. 86716 
3- 86295 
3. 85869 


4. 84421 
4.83912 

4- 83395 
4. 82869 
4. 82336 


5.81306 
5- 80695 
5- 80074 
5- 79443 
5- 78803 


6. 78190 
6. 77477 
6. 76753 
6. 76017 
6.75271 


7- 75074 
7- 74259 
7- 73432 
7- 72591 
7-71738 


8.71959 
8. 71042 
8. 701 1 1 
8.69165 
8. 68206 


11° 00' 


• 96359 


I. 92718 


2. 89077 


3- 85436 


4- 81795 


5- 78154 


6. 74513 


7. 70872 


8. 67232 


10' 
20' 
30' 

50^ 


. 96249 
. 96138 
.96025 

•959" 
• 95795 


I. 92498 
1.92276 
I. 92051 
I. 91822 
I. 91590 


2. 88748 
2. 88414 
2. 88076 
2. 87732 
2. 87385 


3- 84997 
3- 84552 
3. 84101 

3- 83643 
3.83180 


4.81247 
4. 80690 
4. 80126 
4- 79553 
4. 78974 


5- 77496 
5. 76828 
5- 76152 

5-75464 
5- 74769 


6. 73746 
6. 72966 
6.72177 
6. 71375 
6. 70564 


7- 69995 
7. 69104 
7. 68202 
7. 67286 
7- 66358 


8. 66245 
8. 65242 
8. 64227 
8.63196 
8.62153 


12° oo' 


• 95677 


I- 91355 


2. 87032 


3. 82709 


4- 78386 


5-74063 


6. 69741 


7. 65418 


8. 61095 


10' 

20' 
3C/ 
40^ 
50' 


• 95558 

• 95438 

• 95315 
•95192 

• 95066 


I. 91116 
1.90876 
I. 90631 
I. 90384 
I. 90132 


2. 86674 
2.86313 
2. 85946 
2. 85575 
2. 85199 


3- 82232 
3- 81750 
3. 81261 
3. 80766 
3.80265 


4. 77790 
4- 77187 
4- 76576 
4- 75958 
4- 75332 


5- 73348 
5. 72625 
5- 71892 
5-71150 
5- 70399 


6. 68906 
6. 68062 
6.67207 
6. 66341 
6. 65465 


7- 64464 
7- 63500 
7. 62522 

7- 61533 
7. 60532 


8. 60023 
8. 58938 
8.57838 
8. 56724 
8.55598 


13° 00' 


• 94940 


I. 89880 


2.84820 


3- 79759 


4. 74698 


5. 69638 


6. 64577 


7-59516 


8. 54456 


ic/ 
20' 

30' 
40' 
50' 


. 9481 1 
. 94682 

• 94550 

• 94417 

• 94283 


I. 89623 
I. 89364 
I. 891.01 
1.88835 
I. 88566 


2. 84434 
2.84045 
2.83651 
2. 83252 
2. 82849 


3- 79245 
3- 78726 
3. 78201 
3- 77669 
3-77132 


4. 74056 
4- 73407 
4. 72751 
4. 72087 

4- 71415 


5. 68868 
5. 68088 
5-67301 
5- 66505 
5- 65698 


6. 63679 
6. 62770 
6.61852 
6. 60922 
6. 59981 


7- 58491 
7- 57452 
7- 56402 
7- 55339 
7- 54264 


8. 53302 
8.52133 
8- 50952 
8- 49757 
8. 48548 


14° 00' 


• 94147 


1.88295 


2. 82442 


3- 76589 


4. 70736 


5- 64884 


6. 59031 


7-53179 


8. 47326 



APPENDIX 7. A PLANE TABLE MANUAL. 



333 



Table of coefficiejits for reducing readings of inclined sights on a vertical rod to ho7-izontal 

distance — Concluded.. 



Angle of 
inclina- 
tion 


Horizontal projection of 


I m. 


2 m. 


3 m. 


4 m. 


S m. 


6 ni. 


7 m. 


8 m. 


9 m. 


10' 
20'' 
30' 
40' 
50' 


. 94010 
•93871 

• 93731 

• 93589 
■93446 


I. 88020 
I. 87742 
I. 87462 
I. 87178 
I. 86892 


2.82030 
2.81613 
2.81192 
2. 80767 
2. 80338 


3. 76040 

3- 75484 
3- 74923 
3- 74356 
3- 73784 


4. 70050 
4. 69355 
4, 68654 

4. 67945 
4. 67229 


5. 64060 
5. 63226 
5. 62385 

5- 61534 
b- 60675 


6. 58070 
6. 67097 
6. 56115 

6.55123 
6. 54121 


7. 52080 
7. 50968 
7. 49846 
7.48712 
1- 47567 


8. 46090 
8. 44840 
8. 43578 
8. 42302 
8. 41013 


15° OO' 


• 93301 


I. 86602 


2. 79903 


3^ 73204 


4. 66505 


5.59806 


6. 53107 


7. 46408 


8.39710 


16° 00' 


. 92402 


I. 84805 


2.77208 


3. 69610 


4. 6201 1 


5^ 54414 


6. 46816 


7. 39218 


8. 31620 


17° 00' 


. 91452 


I. 82904 


2. 74355 


3. 65806 


4.57258 


5.48710 


6. 40161 


7. 31613 


8. 23065 


18° 00' 


•90451 


I. 80902 


2.71352 


3. 61803 


4- 52253 


5.42704 


6. 33154 


7.23605 


8. 14056 


19° 00' 


. 89400 


I. 78800 


2.68201 


3. 57600 


4. 47001 


5. 36402 


6. 25802 


7. 15203 


8. 04603 


20° OO' 


. 88302 


I. 76604 


2. 64906 


3.53208 


4. 41510 


5. 29812 


6. 18114 


7. 06416 


7.94718 



334 COAST AND GEODETIC SURVEY REPORT, 1905. 

Table T. — Table showing the height in feet corresponding to a given ayigle of elevation 

and a given distance in meters.'^ 



Meters 


300 


400 


500 


600 


700 


800 


900 


1 000 


1 100 


1200 


1300 


1400 


1500 


1600 


1700 


1800 


1900 


2000 


Angle 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


Feel 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


\Feet 


'^eet 


i' 


0.3 


0.4 


0.6 


0.6 


0.8 


0.9 


1.0 


1.2 


1-3 


1-5 


1-7 


1.8 


2.0 


■2.1 


2.3 


2.5 


2.7 


2.8 


2 


0.6 


0.8 


I.O 


1.2 


1-5 


1.7 


1-9 


2, 1 


2.4 


2.6 


2.9 


3.1 


3.4 


3-7 


3-9 


4.2 


4-5 


4-7 


3 


0,9 


I. 2 


1.5 


1.8 


2.2 


2.5 


2.8 


3-1 


3.4 


3-8 


4.2 


4-4 


4.8 


5-3 


5.6 


5.9 


6-3 


6.6 


4 


1.2 


1-5 


2.0 


2.4 


2.8 


3.2 


3.6 


4.1 


4-5 


4.9 


5-4 


5.8 


6.3 


6.8 


7-2 


7.6 


8.1 


8.6 


5 


1-5 


1-9 


2.4 


2.9 


3-5 


4.0 


4.5 


5-0 


5-5 


6.1 


6.6 


7-1 


7-7 


8.3 


8.8 


9-4 


9-9 


10-5 


6 


1.8 


2.3 


2.9 


3-5 


4.2 


4.8 


5-3 


5.9 


6.6 


7.2 


7.9 


8.5 


9-1 


9.8 


10.4 


II. I 


11.7 


12.4 


7 


2. I 


2.7 


3.4 


4-1 


4.8 


5-5 


6.2 


6.9 


7.6 


8.4 


9-1 


9.8 


10.6 


II.4 


12. 1 


12.8 


13-5 


14-3 ■ 


8 


2.4 


31 


3-9 


4.6 


5-5 


6.3 


7-1 


7.9 


8.7 


9-5 


10.4 


II. I 


12.0 


12.9 


13-7 


14.5 


15-3 


16.2 


9 


2.7 


3-5 


4-4 


5-2 


6.2 


7.0 


7-9 


8.8 


9-7 


10.7 


II. 6 


12.5 


13.4 


14.4 


IS- 3 


16.2 


17.2 


18. 1 


10 


2.9 


3-8 


4.9 


5-8 


6.8 


7.8 


8.8 


9.8 


10.8 


II. 8 


12.8 


13.8 


14.9 


15.9 


16.9 


17.9 


19.0 


20.0 


II 


3-2 


4.2 


5.3 


6.4 


7-5 


8.6 


9.6 


10.7 


II. 8 


13-0 


14. 1 


15.1 


16.3 


17. 5 


18.6 


19.7 


20.8 


21.9 


12 


3.5 


4.6 


5.8 


6.9 


8.2 


9-3 


IO-5 


II. 7 


12.9 


14. 1 


15-3 


16.5 


17.7 


19.0 


20.2 


21.4 


22.6 


23.8 


13 


3.8 


5-0 


6.3 


7-5 


8.8 


10. I 


II. 4 


12.6 


13-9 


15-2 


16.6 


17.8 


19.2 


20.5 


21.8 


23.1 


24.4 


25-7 


14 


4-1 


5-4 


6.8 


8.1 


9-5 


10.9 


12.2 


13.6 


15-0 


16.4 


17.8 


19. 1 


20.6 


22.0 


23-4 


24.8 


26.2 


27.6 


15 


4.4 


5-7 


7.2 


8,6 


10.2 


II. 6 


13-1 


14-5 


16.0 


17-5 


19.0 


20.5 


22.0 


23.6 


25.0 


26.5 


28.0 


29-5 


16 


4-7 


6.1 


7-7 


9.2 


10.8 


12.4 


13-9 


15.5 


17. 1 


18.7 


20.3 


21.8 


23-5 


25.1 


26.7 


28.2 


29-9 


31-4 


17 


4-9 


6.5 


8.2 


9.8 


II. 5 


13- 1 


14.8 


16.5 


18. 1 


19.8 


21.5 


23.1 


24.9 


26.6 


28.3 


30.0 


31.7 


33-4 


18 


5-2 


6,9 


8.7 


10.4 


12.2 


13-9 


15-7 


17.4 


19.2 


21.0 


22.8 


24-5 


26.3 


28.2 


29.9 


31-7 


33-5 


35-3 


19 


5-5 


7-3 


9.1 


10.9 


12.8 


14-7 


16.5 


18.4 


20.2 


22. 1 


24.0 


25.8 


27.7 


29-7 


31-5 


33-4 


35-3 


37-2 


20 


5-8 


7-7 


9.6 


II. .S 


13-5 


15-4 


17-4 


19-3 


21.3 


23.3 


25.2 


27.2 


29.2 


31-2 


33-2 


35- 1 


37-1 


39-1 


21 


6.1 


8.0 


10. 1 


12. I 


14.2 


16.2 


18.2 


20.3 


22.3 


24.4 


26.5 


28.5 


30.6 


32.7 


34-8 


36.8 


38.9 


41.0 


22 


6.4 


8.4 


10.6 


12.6 


14.9 


17.0 


19. 1 


21. 2 


23-4 


25-5 


27.7 


29.8 


32.0 


34.3 


36-4 


38.5 


40.7 


42.9 


23 


6.7 


8,8 


II. I 


13.2 


15- 5 


17.7 


20.0 


22.2 


24.4 


26.7 


29.0 


31.2 


33-5 


35-8 


38.0 


40-3 


42.5 


44.8 


24 


6.9 


9.2 


"•5 


13-8 


16.2 


18.5 


20,8 


23.1 


25-5 


27.8 


30.2 


32.5 


34-9 


37-3 


39-6 


42.0 


44-3 


46.7 


25 


7.2 


9.6 


12.0 


14.4 


16.9 


19-3 


21.7 


24.1 


26.5 


29.0 


31-4 


33.8 


36-3 


38.8 


41-3 


43-7 


46.2 


48.6 


26 


7-5 


9-9 


12.5 


14.9 


17-5 


20.0 


22.5 


25.0 


27.6 


30.1 


32.7 


35-2 


37-8 


40.4 


42.9 


45-4 


48.0 


50.5 


27 


7.8 


10.3 


13-0 


15-5 


18.2 


20.8 


23.4 


26.0 


28.6 


31-3 


33-9 


36.5 


39-2 


41.9 


44-5 


47-1 


49.8 


52.4 


28 


8.1 


10.7 


13- 4 


16. 1 


18.9 


21.5 


24.2 


26.9 


29.7 


32.4 


35-2 


37.8 


40.6 


43-4 


46. 1 


48.8 


51-6 


54-3 


29 


8.4 


II. I 


13-9 


16.7 


19-5 


22.3 


25-1 


27.9 


30.7 


33.6 


36.4 


39-2 


42.1 


45-0 


47-8 


50.6 


53-4 


56-2 


30 


8.7 


"•5 


14.4 


[7.2 


20.2 


23.1 


26.0 


28.9 


31.8 


34-7 


37.6 


40.5 


43-5 


46-5 


49-4 


52.3 


55-2 


58.2 


40 


"■5 


15.3 


19.2 


22.9 


26.9 


30-7 


34-6 


38.4 


42.3 


46. 1 


50.0 


53-9 


57-8 


61.7 


65.6 


69.4 


73-3 


77-3 


50 


14.4 


19. 1 


23-9 


28.7 


33-5 


38.3 


43-2 


47-9 


52.7 


57-6 


62.4 


67.2 


72.1 


77.0 


81.8 


86.6 


91-5 


96.3 


I°00 


17.2 


22.9 


28.7 


34.4 


40.2 


46.0 


51-7 


57-5 


63.3 


69.0 


74.8 


80.6 


86.4 


92-3 


98.0 


104 


no 


115 


I 10 


20. 1 


26.7 


33.5 


40. 1 


46.9 


53.6 


60.3 


67.0 


73.8 


80.5 


87.2 


93-9 


100.7 


107.5 


114- 3 


121 


128 


134 


I 20 


23.0 


30-5 


38.3 


45-8 


53-6 


61.2 


69.0 


76.6 


84.2 


91.9 


99.6 


107-3 


115. 1 


123 


131 


138 


146 


154 


I 30 


25.8 


34-4 


43-0 


51.6 


60.3 


69.0 


77-7 


86.1 


94-7 


103.4 


112. 


120.7 


130 


138 


147 


155 


164 


173 


I 40 


28.7 


38.2 


47.8 


57-3 


66.9 


76.6 


86.3 


95-6 


105.2 


115 


124 


134 


144 


153 


163 


173 


182 


192 


I 50 


31-6 


42.0 


52.6 


63.0 


73.6 


84.2 


94-9 


105.2 


115. 7 


126 


137 


147 


158 


169 


179 


190 


200 


211 


2 GO 


34-4 


45-8 


57-4 


68.9 


80 


92 


103 


115 


126 


138 


149 


161 


172 


184 


195 


207 


218 


230 


2 30 


43-0 


57-3 


71.7 


86.0 


100 


"5 


129 


144 


158 


172 


186 


201 


215 


230 


244 


259 


273 


287 


3 00 


51.6 


68.8 


86.2 


103.2 


120 


138 


155 


172 


190 


207 


224 


241 


259 


276 


293 


310 


328 


345 


3 30 


60.2 


80.4 


100.5 


120.5 


141 


161 


181 


201 


221 


241 


261 


281 


302 


322 


342 


362 


382 


402 


4 00 


68.9 


91.8 


1 14. 8 


137-7 


161 


184 


207 


230 


253 


276 


299 


322 


345 


368 


391 


414 


437 


460 



* Curvature and refraction taken into account for angles of elevation. This table should not be used for angles of 
depression. 



APPENDIX 7. A PLANE TABLE MANUAL. 335 

Example of use of table of heights. 
[Angle of elevation from point A to point B, distant from each other 1756 meters=i° 56'.] 

Meters. Feet, 

I ° 50' 1 700 1 79. 00 

1° 50' 50 5- 26 

1° 50' 6 63 

0° 06'' 1700 10. 40 

0° 06'. .... . 50 29 

0° 06' 6 04 



195.62 

Point B is 195.62 feet above point A. 

Formula for determining heights by a vertical angle and distance. — The difference of 
level consists of two parts — that which ari.ses from the angle of elevation above the 
horizontal plane of the station and that which is due to the curvature of the earth. 
The former depends upon the angle and distance, the latter upon the distance and the 
earth's radius. If a' be the angle of elevation in minutes of arc, d the distance, h the 
height, then, as the tangent of i' is ^^Vt. we have for the first part h = ^^^^a'd, if h 
and d are both expressed in the same units of length, but if d is expressed in meters 
and h in feet, one meter being 3.28 feet, we get h — ^-^-^^a'd. For the fraction joV? we 
may conveniently and with sufficient accuracy put toVo less ^V of tttV > and thus find 
the rule: Multiply the distance in meters by the nujnber of minutes of arc, point off the 
thousandth part, and subtract the twentieth part of the number thus obtained. This will 
give the first portion of difference of height, whether elevation or depression. 

The second term, depending on the curvature, varies as the square of the distance, 
and amounts to 0.22 foot in 1000 meters, including the effect of ordinary refraction. 
As with the instruments under consideration extreme accuracy is not attainable, it is 
plain that for distances under 1000 meters this term may be neglected. When the 
distance is greater, we have the following rule: Take the thousandth part of the distance 
in meters, square the same, having regard to the first decimal figure, and multiply by 
0.22. This term is always positive. If the first term be an elevation, it is increased; if 
a depression, it it diminished by the second term. 

Example. — Distance = 5500 meters; angle of elevation, 36'. 

Tinjo^'X a' = 198-000 ^i^-^d = 5.5 
subtract ^V 9.9 square =30.2 
multiply by 0.22 



first term 188. i — 

second term 6.6 second term 6.64 



sum 1 94. 7= difference of elevation in feet. 

38077°— 16 4 



Jd^ 



COAST AND GEODETIC SURVEY REPORT, 1905. 

Table II. — Table shoiving the height, in meters, corre- 

( Curvature and refraction 





100 


200 


300 


400 


500 


600 


700 


800 


900 


1000 


1 100 


1200 


0° \' 


0.03 


0. 06 


0.09 


0. 13 


0. 16 


0. 20 


0.24 


0. 28 


0.32 


0.36 


0. 40 


0.45 


2 


0. 06 


0. 12 


0. 18 


0. 24 


0.31 


0.37 


0.44 


0.51 


0.58 


0.65 


0.72 


0.79 


3 


0.09 


0. 18 


0.27 


0.36 


0.45 


0.55 


0.64 


0.74 


0.84 


0.94 


I. 04 


I. 14 


4 


0. 12 


0. 24 


0.36 


0.48 


0. 60 


0.72 


0.85 


0.97 


I. ID 


1.23 


1.36 


1.39 


5 


0.15 


0. 29 


, 0.44 


0.59 


0.74 


0. 90 


1.05 


I. 21 


1.36 


1-52 


1.68 


1.84 


0° 6' 


0. 18 


0.35 


0.53 


0. 70 


0.89 


1.07 


1.26 


1-44 


1.62 


I. 81 


2. 00 


2. 19 


7 


0. 20 


0.41 


0. 62 


0.82 


I. 04 


1.24 


1.46 


1.67 


1.89 


2. 10 


2.32 


2.44 


8 


0.23 


0.47 


0. 70 


0.94 


1. 18 


1.42 


1.66 


I. 90 


2.16 


2-39 


2.64 


2.89 


9 


0. 26 


0.53 


0.79 


1.06 


1-33 


1-59 


1.87 


2.14 


2.41 


2.68 


2. 96 


3-24 


10 


0. 29 


0.58 


0.88 


1.18 


1-47 


1.77 


2. 07 


2.37 


2.68 


2.98 


3-28 


3-59 


0° II' 


0.32 


0.64 


0.97 


I. 29 


1.62 


1-94 


2. 27 


2. 60 


2.93 


3.27 


3.60 


3-74 


12 


0.35 


0. 70 


1.05 


1. 41 


1.76 


2. 12 


2.48 


2.84 


3-20 


3.56 


3.92 


4.29 


13 


0.38 


0. 76 


1. 14 


1-52 


I. 91 


2. 29 


2.68 


3-07 


3-46 


3-85 


4.24 


4-63 


14 


0.41 


0.82 


1.23 


1.64 


2.05 


2.47 


2.88 


3-30 


3-72 


4-14 


4.56 


4-98 


15 


0.44 


0.88 


1.32 


1.76 


2. 20 


2.64 


3.08 


3-53 


3.98 


4-43 


4.88 


5-33 


0° 16' 


0.47 


0.93 


I. 40 


1.87 


2-34 


2.82 


3-29 


3-77 


4.24 


4.72 


5.20 


5.68 


17 


0.50 


0.99 


1-49 


1.99 


2-49 


2.99 


3-49 


3-90 


4- 50 


5-01 


5.52 


6.03 


18 


0.52 


1.05 


1-58 


2. ID 


2. 64 


3- 17 


3-70 


4.23 


4-77 


5.30 


5.84 


6.38 


T9 


0.55 


I. II 


1.66 


2.22 


2.78 


3-34 


3-90 


4.46 


5-03 


5-59 


6.16 


6.63 


20 


0.58 


I. 17 


1-75 


2.34 


2.93 


3-51 


4. II 


4.70 


5-29 


5-88 


6.48 


7.08 


0° 21' 


0. 61 


■ 1.23 


1.84 


2-45 


3-07 


3-69 


4-31 


4-93 


5-55 


6.17 


6.80 


7-43 


22 


0.64 


1.28 


1-93 


2.57 


3.22 


3-86 


4-51 


5.16 


5-81 


6-47 


7.12 


7.78 


23 


0.67 


1-34 


2. 01 


2.69 


3-36 


4.04 


4.72 


5- 40 


6.08 


6.76 


7.44 


8. 12 


24 


0. 70 


I. 40 


2. 10 


2.80 


3-50 


4.21 


4-92 


5.63 


6.34 


7.05 


7.76 


8.47 


25 


0.73 


1.46 


2.19 


2. 92 


3-65 


4.39 


5-12 


5-88 


6.60 


7-34 


8.08 


8.82 


0° 26' 


0. 76 


1.52 


2.28 


3-04 


3.80 


4.56 


5-33 


6.09 


6.86 


7.63 


8.40 


9.17 


27 


0.79 


1-57 


2.36 


3-15 


3-95 


4-74 


5-53 


6.33 


7.12 


7.92 


8.72 


9.52 


28 


0.82 


1.63 


2-45 


3-27 


4.09 


4.91 


5-74 


6-56 


7-38 


8.21 


9.04 


9.87 


29 


0.84 


I. 69 


2.54 


3.38 


4.24 


5.08 


5-94 


6-79 


7-65 


8-50 


9-36 


10. 22 


30 


0.87 


1-75 


2.62 


3-50 


4-38 


5.26 


6. 14 


7.02 


7.91 


8.79 


9.68 


10.57 


0= 40' 


I. 16 


2-33 


3-50 


4-66 


5-84 


7.00 


8. 18 


9-35 


10.53 


II. 70 


12.88 


14. 06 


50 


1.45 


2. 91 


4-37 


5-83 


7.29 


8.75 


10. 22 


11.68 


13-14 


14.62 


16.08 


17-55 


I 00 


1-75 


3-49 


5-24 


6-99 


8.74 


10.50 


12.25 


14.01 


15-76 


17-52 


19.28 


21. 04 


I 10 


2. 04 


4.08 


6. 12 


8. 16 


10. 20 


12. 24 


14.29 


16.33 


18.38 


20.43 


22.48 


24.53 


I 20 


2-33 


4.66 


6-99 


9-32 


11.66 


13-99 


16.33 


18.66 


21.00 


23-34 


25.68 


28. 03 


1° 30' 


2. 62 


5-24 


7.86 


10.48 


13. II 


15-73 


18.36 


20.99 


23-62 


26.25 


28.88 


31-52 


I 40 


2. 91 


5.82 


8-74 


11.65 


14.56 


17.48 


20. 40 


23-32 


26. 24 


29. 16 


32.09 


35- 01 


I 50 


3.20 


6.40 


9. 61 


12.82 


16.02 


19.23 


22.44 


25.65 


28.86 


32.08 


35-29 


38-51 


2 00 


3-49 


6.99 


10.48 


13-98 


17.49 


20.98 


24.48 


27.98 


31-48 


34.99 


38-49 


42. 00 


2° 30' 


4-37 


8.74 


13. II 


17.28 


21.85 


26. 22 


30.60 


34-97 


39-35 


43-73 


48. II 


52.49 


3 00 


5.24 


10. 48 


15-73 


20.97 


26. 22 


31-47 


36.72 


41-97 


47.22 


52.47 


57-73 


62.99 


3 30 


6.12 


12. 24 


18.36 


24.48 


30. 60 


36.72 


42.85 


44-97 


55.10 


61-23 


67.36 


73-49 


4 00 


6.99 


13-99 


20.98 


27.98 


34- 98 


41.98 


48.98 


55.98 


62.99 


69.99 


77.00 


84.01 




100 


200 


300 


400 


500 


600 


700 


800 


9C0 


1000 


1 100 


1200 



, * Curvature and refraction taken into account for angles of 



APPENDIX 7. A PLANE TABLE MANUAL. 
sponding to given ajigles of elevation ajid distances in meters.'^ 
taken into account. ) 



337 



1300 


1400 


1500 


1600 


1700 


1800 


1900 


2000 


2100 


2200 


2300 


2400 


2500 




0.49 


0.54 


0.59 


0.64 


0. 69 


0.74 


0.80 


0.85 


0. 90 


0.96 


1.02 


1.08 


1.14 


0° \' 


0.87 


0.95 


1. 02 


1. 10 


1. 18 


1.26 


1.35 


1-43 


1.52 


1.60 


I. 69 


1.78 


1.87 


2 


1-25 


1-35 


I. 46 


1-57 


1.68 


1.79 


I. 90 


2. 01 


2.13 


2.24 


2.36 


2.48 


2.60 


3 


1.63 


1.76 


I. 90 


2.03 


2.17 


2.31 


2.45 


2-59 


2.74 


2.88 


3.03 


3.18 


3-33 


4 


2.00 


2.17 


2-33 


2.50 


2.67 


2.83 


3.00 


3.18 


3.35 


3.52 


3.70 


3.88 


4-05 


5 


2.38 


2-57 


2-77 


2. 96 


3-16 


3-35 


3.56 


3.76 


3.96 


4. 16 


4.37 


4.57 


4.78 


0° (>' 


2.76 


2.98 


3.20 


3.43 


3-66 


3-88 


4. II 


4-34 


4.57 


4.80 


5- 04 


5-27 


5.51 


7 


3-14 


3-39 


3-64 


3-89 


4- 15 


4-50 


4.66 


4.92 


5.18 


5.44 


5.70 


5-97 


6. 24 


8 


3-52 


3.80 


4.08 


4.36 


4-64 


4-93 


5.22 


5-50 


5.79 


6.08 


6.37 


6.67 


6.96 


9 


3-90 


4. 20 


4-51 


4.82 


5- 14 


5-45 


5.77 


6.08 


6. 40 


6.72 


7.04 


7.36 


7.69 


10 


4.27 


4. 61 


4-95 


5.29 


5.63 


5-98 


6.32 


6.67 


7. 01 


7.36 


7.71 


8.06 


8.42 


0° 11' 


4-65 


5.02 


5-39 


5.76 


6.13 


6.50 


6.87 


7-25 


7.62 


8.00 


8.38 


8.76 


9. 14 


12 


5-03 


5-42 


5.82 


6. 22 


6.62 


7.02 


7.43 


7.83 


8.24 


8.64 


9-05 


9.46 


9.87 


13 


5-41 


5-83 


6.26 


6.69 


7.12 


7-55 


7.98 


8.41 


8.85 


9.28 


9-72 


10. 16 


10. 60 


14 


5.78 


6.24 


6. 70 


7-15 


7.62 


8.07 


8.53 


8-99 


9.46 


9.92 


10-39 


10.86 


11.32 


15 


6. 16 


6.65 


7.13 


7.62 


8. II 


8-59 


9.08 


9-58 


10.07 


10.56 


11.06 


11-55 


12.05 


0° 16' 


6.54 


7-05 


7.56 


8.08 


8.60 


9. 12 


9.64 


10. 16 


10.68 


II. 20 


11-73 


12.25 


12.78 


17 


6. 92 


7.46 


8.00 


8.55 


9.09 


9.64 


10.19 


10.74 


II. 29 


11.84 


12. 40 


12.95 


13.51 


18 


7-30 


7.87 


8.44 


9.01 


9.59 


10. 16 


10.74 


11.32 


II. 90 


12.48 


13-06 


13- 65 


14.23 


19 


7.68 


8.28 


8.88 


9.48 


10. 08 


10.69 


11. 30 


II. 90 


12.51 


13.12 


13-73 


14.35 


14.96 


20 


8.05 


8.68 


9-31 


9.94 


10.58 


II. 21 


11.85 


12.48 


13- 12 


13.76 


14.40 


15.04 


15. 69 


0° 21^ 


8.43 


9.09 


9-75 


10. 41 


11.07 


11.74 


12. 40 


13.07 


13-73 


14.40 


15-07 


15.74 


16.42 


22 


8.81 


9-50 


10. 19 


10.88 


11.57 


12. 26 


12.95 


13.65 


14-34 


15-04 


15.74 


16.44 


17.14 


23 


9. 19 


9.90 


10. 62 


ir. 34 


12. 06 


12.78 


13.51 


14.23 


14-96 


15.68 


16. 41 


17. 14 


17.87 


24 


9-57 


10.31 


11.06 


II. 81 


12.56 


13-31 


14. 06 


14.81 


15-57 


16.32 


17.08 


17.84 


18. 60 


25 


9-94 


10.72 


11.50 


12. 27 


13.05 


13-83 


14. 61 


15.39 


16. 18 


16.96 


17.75 


18.54 


19.32 


0° 26' 


10.32 


II. 13 


11-93 


12.74 


13.55 


14-35 


15. 16 


15.98 


16.79 


17. 60 


18.42 


19.23 


20.05 


27 


10. 70 


11-53 


12.37 


13.20 


14.04 


14.88 


15.72 


16.56 


17.40 


18. 24 


19.09 


19- 93 


20.78 


28 


11.08 


11.94 


12.80 


13.67 


14.53 


15.40 


16. 27 


17. 14 


18.01 


18.88 


19.76 


20.63 


21.51 


29 


11.46 


12.35 


13-24 


14.13 


15.03 


15.92 


J 6. 82 


17.72 


18.62 


19-52 


20. 42 


21-33 


22.23 


30 


15-24 


16.42 


17. 60 


18.79 


19.97 


21. 16 


22.35 


23-54 


24.73 


25.82 


27 12 


28.31 


29-50 


0° 40' 


19. 02 


20.49 


21.97 


23.44 


24.92 


26. 40 


27.88 


29.36 


30.84 


32.32 


33-81 


35 29 


36-78 


50 


22.81 


24-57 


26.33 


28. 10 


29.87 


31.64 


33-41 


35-18 


36-95 


38.72 


40.50 


42.28 


44.06 


1 00 


26.59 


28.64 


30.70 


32.75 


34.81 


36.87 


38.94 


41.00 


43.06 


45- 13 


47.19 


49.26 


51.33 


I 10 


30.37 


32.72 


35-06 


37.41 


39.76 


42. 10 


44-46 


46.82 


49- 17 


51-53 


53.89 


56.25 


58.61 


I 20 


34.16 


36-79 


39-43 


42.07 


44.71 


47-35 


49-99 


52.64 


55.28 


57-93 


60.58 


63-23 


65.88 


1° 30' 


37-94 


40.87 


43.80 


46.73 


49. 66 


52.59 


55-52 


58.46 


61. 40 


64.34 


67.28 


70. 22 


73. 16 


I 40 


41.72 


44-94 


48.16 


51.38 


54.61 


57.83 


61. 06 


64.28 


67.51 


70.74 


73-97 


77-21 


80. 44 


1 50 


45-50 


49.02 


52.53 


56.04 


59.56 


63.07 


66.59 


70. 10 


73.63 


77- 15 


80.67 


84. 20 


87.72 


2 00 


56.87 


61.26 


65.64 


70.03 


74.42 


78.81 


83.20 


87.59 


91.98 


96-38 


100. 78 


105. 17 


109. 57 


2° 30' 


68.24 


73-51 


78.76 


84.02 


89.29 


94-55 


99.82 


105. 10 


110.35 


115-62 


120. 89 


126. 16 


131.44 


3 00 


79-63 


85.76 


91.89 


98.03 


104. 18 


110.31 


116.45 


122.59 


128. 74 


134- 88 


141.03 


147. 18 


153. 33 


3 30 


91.02 


98.03 


105. 04 


112. 06 


117.07 


126.09 


133- 10 


140. 12 


147. 14 


154. 18 


161. 19 


168. 21 


175- 24 


4 00 


1300 


1400 


1500 


1600 


1700 


1800 


1900 


2000 


2100 


2200 


2300 


2400 


2500 





elevation. This table should not be used for angles of depression. 



338 



COAST AND GEODETIC SURVEY REPORT, 1905. 



Illustration 34 is a diagram showing the method of constructing a scale for taking 
off the heights corresponding to a given angle and distance. 

Table of factors for computing differences in elevation.'^ 

To obtain the difference in elevation in feet multiply the horizontal distance in meters by the 
factor in this table corresponding to the observed angle of elevation or depression. The factors are 
given for each ten minutes, but the value for the nearest minute may be interpolated, using the column 
of differences for one minute. The result is still to be corrected where necessary for the effect of 
curvature and refraction. 

Table III. 



















Diflfer- 


















eiice for 


Angle 


0' 


10' 


20' 


30' 


40' 


50' 


60' 


I minute 

(fourth 

decimal 

place) 






0. 0000 


0.0095 


0. 0191 


0. 0286 


0. 0382 


0. 0477 


0. 0573 


9-5 


I 


0. 0573 


0. 0668 


0. 0764 


0. 0859 


0. 0955 


0. 1050 


0. 1 146 


9-6 


2 


0. 1 146 


0. 1 241 


0. 1337 


0. 1432 


0. 1528 


0. 1624 


0. 1719 


9-6 


3 


0. 1719 


0. 1815 


0. 1911 


0. 2007 


0. 2102 


0. 2198 


0. 2294 


9.6 


4 


0. 2294 


0. 2390 


0. 2486 


0. 2582 


0. 2678 


0. 2774 


0. 2870 


9-6 


5 


0. 2870 


0. 2967 


0. 3063 


0.3159 


0. 3255 


0. 3352 


0. 3448 


9-6 


6 


0. 3448 


0. 3545 


0.3641 


0.3738 


0. 3835 


0. 3932 


0. 4028 


9-7 


7 


0. 4028 


0.4125 


0. 4222 


0.4319 


0. 4416 


0.4514 


0. 4611 


9-7 


8 


0.461 1 


0. 4708 


0. 4806 


0. 4903 


0. 5001 


0. 5098 


0. 5196 


9.8 


9 


0.5196 


0. 5294 


0. 5392 


0. 5490 


0. 5588 


0. 5687 


0. 5785 


9-8 


10 


0. 5785 


0. 5884 


0. 5982 


0.6081 


0.6179 


0. 6278 


0. 6377 


9-9 


II 


0. 6377 


0. 6476 


0. 6576 


0. 6675 


0. 6774 


0. 6874 


0. 6974 


9-9 


12 


0. 6974 


0. 7073 


0.7173 


0. 7273 


0. 7374 


0. 7474 


0. 7574 


10. 


13 


0. 7574 


0. 7675 


0. 7776 


0. 7877 


0. 7978 


0. 8079 


0.8180 


10. 1 


M 


0. S180 


0.8282 


0. 8383 


0. 8485 


0. 8587 


0. 8689 


0. 8791 


10. 2 


15 


0. 8791 


0. 8893 


0. 8996 


0. 9099 


0. 9201 


0. 9304 


0. 9408 


10.3 


16 


0. 9408 


0.951 1 


0. 9615 


0. 9718 


0. 9822 


0. 9926 


I. 0031 


10. 4 


17 


1-0031 


I- 0135 


I. 0240 


1.0344 


1.0449 


1-0555 


I. 0660 


10.5 


18 


I. 0660 


I. 0766 


I. 0872 


I. 0978 


I. 1084 


1. 1190 


I. 1297 


10. 6 


19 


1. 1297 


I. 1404 


I. 1511 


I. 1618 


I. 1726 


I- 1833 


I. 1941 


10.7 


20 


I. 1941 


I . 2050 


I. 2158 


I. 2266 


I- 2375 


I- 2485 


I- 2594 


10. 9 


21 


I- 2594 


I. 2704 


I. 2813 


1.2924 


I- 3034 


I- 3144 


I- 3255 


II. 


22 


1-3255 


I- 3367 


I- 3478 


1-3590 


I. 3702 


I. 3814 


I. 3926 


II. 2 


23 


1.3926 


1-4039 


1-4152 


I. 4266 


I- 4379 


I- 4493 


I. 4607 


II. 4 


24 


I. 4607 


I. 4722 


1.4836 


I- 4952 


I. 5067 


I. 5183 


I- 5299 


"■5 


25 


1.5299 


I- 5415 


I- 5532 


I- 5649 


I- 5766 


r- 5884 


1.6002 


11.7 


26 


I. 6002 


1. 6120 


I. 6239 


I- 6358 


1.6477 


1-6597 


1-6717 


II. 9 


27 


1-6717 


1.6837 


I. 6958 


I. 7079 


I. 7200 


I. 7322 


1-7444 


12. I 


28 


1.7444 


I. 7567 


1 . 7690 


I. 7814 


I- 7937 


I. 8061 


I. 8186 


12.4 


29 


I. 8186 


1.8311 


I. 8436 


I. 8562 


1.8688 


I. 8815 


I. 8942 


12.6 


30 


I. 8942 


I. 9069 


I. 9197 


I. 9326 


I- 9454 


1-9584 


I- 9713 


12.9 


31 


I -9713 


I- 9843 


I- 9974 


2. 0105 


2. 0236 


2. 0368 


2. 0501 


13- 1 


32 


2. 0501 


2. 0634 


2. 0767 


2.0901 


2. 1036 


2. 1171 


2. 1306 


13-4 


33 


2. 1306 


2. 1442 


2- 1578 


2. 1715 


2- 1853 


2. 1991 


2.2130 


1.3-7 


34 


2. 2130 


2. 2269 


2. 2408 


2. 2548 


2. 2689 


2. 2831 


2. 2973 


14.0 


35 


2. 2973 


2.3115 


2. 3258 


2. 3402 


2. 3546 


2.3691 


2. 3837 


14.4 


36 


2.3837 


2. 3983 


2.4130 


2.4277 


2. 4425 


2. 4574 


2.4723 


14.8 


37 


2.4723 


2. 4873 


2. 5023 


2.5175 


2. 5327 


2. 5479 


2- 5633 


15-2 


38 


2. 5633 


2- 5787 


2. 5942 


2. 6097 


2.6253 


2. 6410 


2. 6568 


15.6 


39 


2. 6568 


2. 6726 


2. 6885 


2- 7045 


2. 7206 


2. 7367 


2. 7530 


16.0 


40 


2. 7530 


2. 7692 


2. 7856 


2. 8021 


2.8186 


2. 8353 


2. 8520 


16.5 


41 


2. 8520 


2. 8688 


2. 8857 


2. 9026 


2. 9197 


2. 9368 


2. 9541 


17.0 


42 


2.9541 


2.9714 


2.9888 


3-0063 


3- 0239 


3. 0416 


3- 0594 


17.6 


43 


3- 0594 


3- 0773 


3-0953 


3- "34 


3- 1316 


3- 1499 


3- 1683 


18. I 


44 


3- 1683 


3. 1868 


3- 2054 


3. 2241 


3. 2429 


3. 2618 


3. 2808 


18.8 



* Computed by G. R. Putnam, Assistant, Coast and Geodetic Surs'ey. 



APPENDIX 7. A PLANE TABLE MANUAL. 



339 



Table of corrections for acrvatiire and refraction.'^ 

The correction in feet for the combined effect of curvature and refraction is given for each 100 
meters' distance, the thousands of meters being given in the column to the left and the hundreds in 
the upper line. The correction is to be added to the difference of elevation for angles of elevation 
and subtracted for angles of depression, or it is alvyays to be added to the uncorrected elevation of the 
point to be determined from point of observation. 

Example: At a station whose elevation is 1000 feet (at telescope), angle to signal=3° elevation, 
horizontal distance=50oo meters. From Table III factor is 0.17 19, which multiplied by 5000=859.5 
feet. From Table IV correction is 5.5 feet. Corrected difference of elevation=859.5+5.5=865 feet, 
which added to 1000=1865 feet for elevation of signal. If the above angle to signal be 3° depres- 
sion, then corrected difference of elevation=859. 5— 5.5=854 feet, which makes height of signal= 
1000—854=146 feet. 

Tabi<e IV. 



Distance in 
meters 





100 


200 


300 


400 


500 


600 


700 


800 


900 


1000 




Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 


Feet 





0.0 


0.0 


0. 


0. 


0. 


0. I 


0. I 


0. I 


0. 1 


0. 2 


0. 2 


1000 


0. 2 


0-3 


0.3 


0.4 


0.4 


0.5 


0.6 


0.6 


0.7 


6.8 


0.9 


2000 


0.9 


I.O 


I. I 


I. 2 


1-3 


1-4 


1-5 


1.6 


1-7 


1-9 


2.0 


3000 


2.0 


2. I 


2.3 


2.4 


2.6 


2.7 


2.9 


3-0 


3-2 


3-4 


3-5 


4000 


3-5 


3-7 


3-9 


4.1 


4-3 


4-5 


4.7 


4-9 


51 


5-3 


5-5 


5000 


5-5 


5.8 


6.0 


6.2 


6.5 


6.7 


7.0 


7.2 


■ 7-4 


7-7 


8.0 


6000 


8.0 


8.2 


8.5 


8.8 


9-1 


9-4 


9-7 


10. 


10.2 


10.6 


10. 9 


7000 


10.9 


II. 2 


II. 5 


II. 8 


12. I 


12.5 


12.8 


13- I 


13-5 


13.8 


14.2 


8000 


14.2 


14-5 


14.9 


15-3 


15.6 


16. 


16.4 


16.8 


17.2 


17.6 


18.0 


9000 


18.0 


18.4 


18.8 


19. 2 


19. 6 


20.0 


20. 4 


20.8 


21.3 


21.7 


22. 2 


lOOOO 


22. 2 


22.6 


23.0 


23-5 


24. 


24.4 


24.9 


25.4 


25.8 


26.3 


26.8 


IIOOO 


26.8 


27.3 


27.8 


28.3 


28.8 


29-3 


29.8 


30.3 


30.8 


31-4 


31-9 


12000 


31-9 


32.4 


33- 


33-5 


34-1 


34.6 


35-2 


35-7 


36.3 


36.9 


37-4 


13000 


37-4 


38.0 


38.6 


39-2 


39-8 


40.4 


41. 


41.6 


42. 2 


42.8 


43-4 


14000 


43-4 


44-1 


44-7 


45-3 


46.0 


46.6 


47.2 


47-9 


48.5 


49-2 


49.8 


15000 


49.8 


50.5 


51-2 


51-9 


52.5 


53-2 


53-9 


54-6 


55-3 


56.0 


56.7 


16000 


56.7 


57-4 


58.2 


58.9 


59-6 


60.3 


61. 


61.8 


62.5 


63.3 


64.0 i 


17000 


64.0 


64.8 


65.6 


66.3 


67.1 


67.9 


68.6 


69.4 


70. 2 


71.0 


71.8 i 


18000 


71.8 


72.6 


73-4 


74.2 


75- 


75.8 


76.7 


77-5 


78.3 


79.1 


80.0 


19000 


80.0 


80.8 


81.7 


82.5 


83.4 


84.2 


85.1 


86.0 


86.9 


87.7 


88.6 



* Computed by G. R. Putnam, Assistant, Coast and Geodetic Survey. 



340 



COAST AND GEODETIC SURVEY REPORT, 1905. 



Table of factors for computing differences in elevation. 

To obtain the difference in elevation in meters, multiply the horizontal distance in meters by the 
factor in this table corresponding to the observed angle of elevation or depression. The factors are 
given for each ten minutes, but the value of the nearest minute may be interpolated, using the column 
of differences for one minute. The result is still to be corrected where necessary for the effect of 
curvature and refraction. 

Tabi,e; V. 



















Difference 


Angle 


0' 


10' 


20' 


30' 


40' 


50' 


60' 


for I min- 
ute (4th dec. 
place) 






0. 0000 


0.0029 


0. 0058 


0.0087 


0. ori6 


0. 0145 


0.0175 


2.9 


I 


• 0175 


. 0204 


.0233 


.0262 


.0291 


.0320 


•0349 


2 


9 


2 


■0349 


.0378 


.0407 


•0437 


.0466 


•0495 


.0524 


2 


9 


3 


.0524 


.0553 


.0582 


.0612 


.0641 


. 0670 


.0699 


2 


9 


4 


.0699 


.0729 


.0758 


.0787 


.0816 


.0846 


•0875 


2 


9 


5 


.0875 


.0904 


•0934 


.0963 


. 0992 


. 1022 


• 105 1 


2 


9 


6 


.1051 


. 1080 


.1110 


•1139 


. 1 169 


.1198 


. 1228 


2 


9 


7 


.1228 


• 1257 


.1287 


•1317 


.1346 


•1376 


.1405 


2 


9 


8 


.1405 


•1435 


.1465 


•1495 


• 1524 


•1554 


.1584 


3 





9 


.1584 


. 1614 


. 1644 


•1673 


•1703 


•1733 


■ 1763 


3 





10 


• 1763 


•1793 


.1823 


•1853 


.1883 


.1914 


• 1944 


3 





II 


.1944 


•1974 


. 2004 


•2035 


.2065 


■2095 


. 2126 


3 





12 


. 2126 


.2156 


.2186 


.2217 


.2247 


.2278 


.2309 


3 





13 


.2309 


•2339 


.2370 


. 2401 


• 2432 


. 2462 


■2493 


3 


I 


14 


•2493 


• 2524 


• 2555 


• 2586 


. 2617 


.2648 


.2679 


3 


1 


15 


.2679 


. 2711 


.2742 


•2773 


• 2805 


.2836 


.2867 


3 


I 


16 


.2867 


•2899 


.2931 


. 2962 


•2994 


.3026 


• 3057 


3 


2 


17 


•3057 


.3089 


. 3121 


•3153 


• 3185 


.3217 


•3249 


3 


2 


18 


■3249 


.3281 . 


•3314 


•3346 


■3378 


■3411 


•.3443 


3 


2 


19 


•3443 


•3476 


•3508 


•354i 


■3574 


.3607 


.3640 


3 


3 


20 


.3640 


•3673 


.3706 


•3739 


• 3772 


■3805 


•3839 


3 


3 


21 


.3839 


.3872 


• 3906 


•3939 


•3973 


.4006 


. 4040 


3 


3 


22 


. 4040 


• 4074 


.4108 


.4142 


.4176 


. 4210 


• 4245 


3 


4 


23 


•4245 


.4279 


■ 4314 


• 4348 


•4383 


•4417 


■ 4452 


3 


4 


24 


• 4452 


• 4487 


.4522 


•4557 


• 4592 


.4628 


.4663 


3 


5 


25 


.4663 


.4699 


• 4734 


•4770 


.4806 


.4841 


■ 4877 


3 


5 


26 


.4877 


•4913 


■ 4950 


.4986 


.5022 


•5059 


■5095 


3 


6 


27 


•5095 


•5132 


.5169 


• 5206 


• 5243 


.5280 


■ 5317 


3 


7 


28 


•5317 


• 5354 


• 5392 


•5430 


• 5467 


•5505 


• 5543 


3 


8 


29 


•5543 


.5581 


.5619 


•5658 


• 5696 


■5735 


• 5774 


3 


8 


30 


.5774 


.5812 


.5851 


.5890 


■5930 


•5969 


. 6009 


3 


9 


31 


.6009 


.6048 


.6088 


.6128 


.6x68 


.6208 


.6249 


4 





32 


.6249 


.6289 


• 6330 


.6371 


.6412 


• 6453 


- 6494 


4 


I 


33 


.6494 


.6536 


• 6577 


.6619 


.6661 


.6703 


• 6745 


4 


2 


34 


•6745 


.6787 


.6830 


.6873 


.6916 


•6959 


. 7002 


4 


3 


35 


. 7002 


.7046 


.7089 


•7133 


• 7177 


. 7221 


.7265 


4 


4 


36 


•7265 


.7310 


•7355 


.7400 


•7445 


.7490 


•7536 


4 


5 


37 


■7536 


.7581 


.7627 


•7673 


.7720 


■7766 


•7813 


4 


6 


38 


• 7813 


.7860 


• 7907 


• 7954 


. 8002 


.8050 


.8098 


4 


7 


39 


.8098 


.8146 


•8195 


• 8243 


.8292 


.8342 


•8391 


4 


9 


40 


•8391 


.8441 


.8491 


• 8541 


• 8591 


.8642 


■8693 


5 





41 


•8693 


. 8744 


.8796 


.8847 


.8899 


•8952 


.9004 


5 


2 


42 


.9004 


.9057 


. 91 10 


•9163 


.9217 


.9271 


•9325 


5 


4 


43 


•9325 


.9380 


•9435 


.9490 


• 9545 


.9601 


• 9657 


5 


6 


44 


•9657 


•9713 


• 9770 


■ 9827 


.9884 


.9942 


I. 0000 


5-7 



APPENDIX 7. A PLANE TABLE MANUAL. 
Table of corrections for curvature and refraction. 



341 



The correction in meters for the combined effect of curvature and refraction is given for each 100 
meters distance, the thousands of meters being given in the column to the left and the hundreds in 
the upper line. The correction is to be added to the difference of elevation for angles of elevation 
and subtracted for angles of depression, or it is always to be added to the uncorrected elevation of 
the point to be determined from point of observation. 

Example: At a station whose elevation is 304.80 meters (at telescope), angle to signal 3° eleva- 
tion, horizontal distance 5000 meters. From Table V factor is 0.0524, which multiplied by 5 000= 
262.00. From Table VI correction is 1.67 meters. Corrected difference of elevation=262.oo-(- 
1.67=263.67 meters, which added to 304.80=568.47 meters for elevation of signal. If the above 
angle to signal be 3° depression, then corrected difference of elevation 262.00—1.67=260.33 meters, 
which makes height of signal=3o4.8o— 260.33=44.47 meters. 

Table VI. 



Distance in 
























meters 





100 


200 


300 


400 


500 


600 


700 


800 


goo 


1000 





0. 00 


0.00 


0.00 


0. 01 


0. 01 


0. 02 


0.02 


0.03 


0.04 


0.05 


0. 07 


1000 


0.07 


0.08 


0. 10 


0. II 


0. 13 


0. 15 


0. 17 


0. 19 


0. 22 


0. 24 


0.27 


2000 


0. 27 


0. 29 


0.32 


0.35 


0.38 


0. 42 


0.45 


0.49 


0.52 


0.56 


0.60 


3000 


0. 60 


0.64 


0.68 


0.73 


0.77 


0.82 


0.86 


0.91 


0. 96 


I. 01 


1.07 


4000 


1.07 


I. 12 


I. 18 


1.23 


I. 29 


1-35 


1. 41 


1-47 


1.54 


\. 60 


1.67 


5000 


I. 67 


1.74 


1.80 


1.87 


1.94 


2. 02 


2.09 


2.17 


2.24 


2.32 


2. 40 


6000 


2.40 


2.48 


2.56 


2.65 


2.73 


2.82 


2.91 


3.00 


3-09 


3-18 


3-27 


7000 


3-27 


3-36 


3-46 


3-55 


3.65 


3-75 


3-85 


3-96 


4.06 


4. 16 


4.27 


8000 


4.27 


4.38 


4-49 


4.60 


4.71 


4.82 


4-93 


5-05 


5.16 


5-28 


5-40 


9000 


5-40 


5-52 


5-65 


5-77 


5-89 


6.02 


6.15 


6.28 


6.41 


6.54 


6.67 


lOOOO 


6.67 


6.80 


6.94 


7.08 


7.22 


7-36 


7-50 


7.64 


7.78 


7-93 


8.07 


1 1000 


8.07 


8.22 


8.37 


8.52 


8.67 


8.82 


8.98 


9-13 


9.29 


9-45 


9.61 


12000 


9.61 


9-77 


9-93 


10.09 


10. 26 


10.42 


10.59 


10.76 


10. 92 


II. 10 


11.27 


13000 


11.27 


11.45 


11.62 


11.80 


11.98 


12. 16 


12.34 


12.52 


12. 71 


12.89 


13.08 


14000 


13.08 


13.26 


13-45 


13.64 


13.83 


14.03 


14. 22 


14.42 


14.61 


14.81 


15.01 


15000 


15.01 


15-21 


15-41 


15.62 


15.82 


16.03 


16.24 


16.44 


16.65 


16.87 


17.08 


16000 


17.08 


17.30 


17-51 


17-73 


17-95 


18. 17 


18.39 


18.61 


18.83 


19-05 


19.28 


17000 


19.28 


19-51 


19-73 


19.96 


20. 19 


20.43 


20.66 


20. 89 


21. 13 


21.37 


21.61 


18000 


21.61 


21.86 


22. 10 


22.34 


22.58 


22.83 


23.08 


23-33 


23-58 


23-83 


24.08 


19000 


24.08 


24-34 


24.60 


24.85 


25. II 


25-37 


25-63 


25-89 


26. 15 


26.42 


26.68 



Compariso7t of feet and meters. 
[i meter =3. 280869 feet.] 



Meters. 


Feet. 


Feet. 


Meters. 


I 


3. 2808 

6. 5617 
9- 8425 

13- 1233 

16. 4042 
19. 6850 

22. 9658 
26. 2467 
29- 5275 


I 

2 


0. 3048 
0. 6096 

0. 9144 

1. 2192 
I. 5240 

1. 8288 
2- 1336 

2. 4384 
2- 7432 


2 


X 


3 


4 


4 : 


1; 


5 


6 ... 


6 


7 




8 


8 


Q . 


q 







NOTE. 

The following illustrations, Nos. 17 to 28, show the conventional signs adopted by 
the United States Geographic Board. 
342 



NO. 17. 



WORKS AND STRUCTURES 



Canal or Ditch- 



Aqueduct or Waterpipe_ 



Aqueduct Tunnel 

Canal Lock (point up stream).. 
Metaled 



Wagon Roads < 



Good .— ,.. - 

Poor or Private 

, On small-scale maps 

Trail or Path 



Railroads { 



[Railroad of any kind_ 
(or Single Track) 

Double Track. 
Juxtaposition o/_. 



Electric 



Jn Wagon Road or Street 
Tunnel 

Railroad Station of any kind 



Steam Electric 



Telegraph Line ^ 



Symbol (modified below) i 
Along road =. 



Along road 

(small-scale maps) 



^Along trail 

Electric Power Transmission Line. 



-1 — I — 1 ; — 1 — ' T" 



-r— i-""r-i--Tr- 



Fences < 



[Fence of any kind — 
(or board fence) 

Stone 

Worm 

Wire 

.Hedge 



Sarbod Smooth 



-rat* /v% t* ^S'S" ft*^ *;* ajo.fl 



NO. 18. 



WORKS AND STRUCTURES 
CONTINUED 



General Symbol . 






Drawbridges (.on large-scale j 

charts leave channel open) \^_ 

Truss ( W. Wood: S. Steel) 









Bridges ) 




Ferries 



(General Symbol 

(or Wagon and Artillery) 




i 



Buildings in general 



Ruins 

Church 

HosoitaL. 



J or + 



Schoolhouse... 
Post Office . 



Telegraph Office 

Waterworks 

Windmill 



..^or^ 



NO. 19. 



WORKS AND STRUCTURES 
CONTINUED 



City, Town, or Village 







City, Town, or Village (generalized) i| 



I Capital 



City, Town, or Village (county Seai ® 

(small-scale maps) 



[other Towns - O 



Cemetery 



: jorL.L 



Mine or Quarry of any kind {or open cut) - » 

Prospect ^ 

Shaft ■■ " 



Mine Tunnel lOpening 

[Showing direction 



Oil Wells 



Oil Tanks {abbreviation OTl. 




Coke Ovens 



NO. 20. 



DRAINAGE 



Streams in general 



Intermittent Streams- 






Lake or Pond in general 

(with or without tint, waterlining, etc J 



Salt Pond [broken shoreline if intermittent). 




Intermittent Lake or Pond. 



Spring 

Falls and Rapids 



y 



Glaciers 



Contours . 

( or as below) 



, Form Lines showing flow 




LETTERING 



Names of natural land features, vertical lettering 
Names of natural water features, slantmg lettering 



NO. 21. 



RELIEF 

( Shown by contours, form lines, or shading as desired) 



Hill Shapes 



Form lines, hachures, 

stipple, 

or other shading 



Contour System 




Depression Contours, if otherwise . 
ambiguous, hachured thus 






Rocky (or use contours) 



Bluffs 



\pther than rocky (or use contours) 




Sand Dunes 



Levee 



««a'.»»»*™""™'»>"*"'*.i»»«» 



NO 22. 



LAND CLASSIFICATION 



/Marsh in general (or Fresh Marsh). Lr ^'^ . ——: =;;: 



Salt.. 



Marsh < 



Wooded.. 



\Cypress Swamp.. 




'«^S^£3?'5.-:f^''k=W'r;s 



S;^'.j^^^EiE?L^ 









W^OOds 0/ any kind {or as shown below). 



Flat green tint 



Woods of any kind (or Broad-Leaved Trees) 






■.■a:.? 



^■Ti-z 






A'ne {or Narrow-Leaved Trees).. 



, » J. f ^ * * . * ■ ^* » J 



T~F 



t** * J« -V 



*C:v;*f.vnO: 



Palm-. 






Palmetto 






4» »asI -5.- 









tts * 



NO. 23. 



LAND CLASSIFICATION 
CONTINUED 



Mangrove 



Bamboo 



Cactus 




Banana „ 


f * 4 ^ f -f f 
+ ^ f -P f V t 







d S <& ^ 


Orchard 


& c? © ?? S 
« B €' -d ^ 






C> © ?5' e <a> 



Grassland in general. 



Tall Tropical Grass.-. 












Cultivated Fields in general. 




NO. 24. 



LAND CLASSIFICATION 
CONTINUED 



Cotton... 






o o o 



'on 



Rice... 



mm 









J.-H; 



Sugar Cane 






Corn—. 



r > -f t. 






BOUNDARIES, 
MARKS. AND MONUMENTS 

National, State, or Province Line 

County Line._. _ _ 



Civil Township, District,.. 
Precinct, or Barrio 

Reservation Line 



Land-Grant Line 

City, Village, or Borough 

Cemetery, Small Park, etc. 



Township, Section, and Quarter Section 
Lines (any one for township line alone, any 
two for township and section lines) 



Township and Section Corners Recovered —+ .^. 4-...- 

Boundary IVIonument ^ 

Triangulation Station a 

Bench mark ._ 



BM 

X 

1232 



U. S. Mineral Monument 



NO. 25. 



HYDROGRAPHY, DANGERS, OBSTRUCTIONS 



Shorelines 



Surveyed 
Unsurveyed 



(Tidal Flats of any kind 
(.or as shown below) 



Rocky Ledges 



Shores ^nd ) g^^^ _ 
Low-Water Lines 



Gravel and Rocks, 



VAfuoL. 



Coral Reefs. 

Kelp.. 

Eel Grass^ ^ 



Rock under water.-. 



Rocl< awash (a/ any stage of the tide).. 
Rocl< whose position is doubtful. 




iilB 


=-s 


1IIIIIIIIIIHIIII!"I|« 

llllllllllllllllliilllf 
llllllllllllllllllllltf 

fi'sr 



1%. 17" 



%y 




* PD 



Rock whose existence is doubtfuL. 



,_, * ED 



NO. 26. 

HYDROGRAPHY, DANGERS. OBSTRUCTIONS 
CONTINUED 



Overfalls and Tide Rips. 
Limiting Danger Line. 



Whirlpools and Eddies... 



V/reck of any kind (or Submerged Derelict) 

Wreck or Derelict not submerged 

Cable (with or without lettering) 

Current, not tidal, velocity 2 knots ^' 



Tidal Currents 



f Flood, I'Aknots jj •<" > 

Ebb, 1 knot ^ *" , 

Flood, 2d hour , or- , , ~ 

\ Ebb. 3d hour . ,, , or , | , ; 



No bottom at 50 Fathoms so so 

Depth Curves 
I Fathom or 6 Foot Line 



2 Fathom or 12 Foot Line. 

3 Fathom or 18 Foot Line. 

4 Fathom Line 

4'/2 Fathom Line 



5 Fathom Line 

6 Fathom Line 

10 Fathom Line........ 

20 Fathom Line....- 

30 Fathom Line 

40 Fathom Line 



SO Fathom Line. 



NO. 27. 

HYDROGRAPHY. DANGERS. OBSTRUCTIONS 



CONTINUED 



100 Fathom Line 

200 Fathom Line.. 
300 Fathom Line 
500 Fathom Line 



1000 Fathom Line... 

2000 Fathom Line 

3000 Fathom Line... 



Abbreviations relating to Bottoms 

M. mud, S. sand, G. gravel, Sh. shells, P. pebbles, Sp. specks, 
CI. clay, St. stones. Co. coral. Oz. ooze, bk. black, wh. white, rd red, 
yl. yellow, gy. gray, bu. blue, dk. dark, It. light, gn. green, br. brown, 
hrd. hard, sft. soft, fne. fine, crs. coarse, rky. rocky, stk. sticky, 
brk. broken, Irg. large, smi. small, stf. stiff, cal. calcareous, dec. 
decayed, rot. rotten, spk.speckled, fly. flinty, gty. gritty, grd. ground, 
str. streaky, vol. volcanic. 



AIDS TO NAVIGATION. ETC. 

Life-saving Station ^ iss (t) 

[(T) indicates telegraphic connection] 

Light of any kind {or Lighthouse). 4: 

Lighthouse, on small scale chart.- — — - • 

Light Vessel of any I<ind- '^ 

Light Vessels shov^ing number of masts ^ 4i A 

Light with Wireless — @ ® 

Light Vessel vjith Wireless...- - (2) 

Light with Submarine Bell :& | 

Light Vessel with Submarine Bell - - -^ 

Light with Submarine Bell and Wireless - — _ (»| ^ 

Light Vessel with Submarine Bell and Wireless — @ 



NO. 28. 



AIDS TO NAVIGATION. ETC. 
CONTINUED 



Beacons 



(Lighted.-. 



. Not lighted-. 

Sectors, shown by dotted lines 



^ >!r 

Bn^ X I i I 1 I 



Abbreviations relating to Lights 



F. fixed. Fig. flashing, Fl, flash, FIs. flashes. Sec. sector. Rev. revolv- 
ing. E. electric. W. white, R. red, V. varied by, Grp. group, Occ, 
occulting. Int. intermittent. Alt alternating, m. 7n//es, min. minutes, 
sec. seconds. 



Buoys < 



Buoy of any kind (or Red Buoy) 

Black 

Striped horizontally ._ 

Striped vertically 

Checkered 

Perch and Square 

Perch and Ball 



Bell ( or use first four symbols with., 
word " bell") 

\Lighted 



M 



Whistling (or use first four symbols il., 

with word " whistling ") 



'♦** 



a! 



Spindle or Stake (.add word" spindle.''. 1 

if space allows) 

Abbreviations relating to Buoys 

G. can, N. nun. S. spar, H. S. horizontal stripes, B. black, R. red, 
W. white, V. S. vertical stripes, G. green, Y. yellow, Ch. checkered. 



Anchorage 



Of any kind (or for large vessels) ^ 



For small vessels.. 



Mooring Buoy 



Range or Tracli Line . 



C5 



0^ 5 



gs 



5 






o 

a. 

'--i TJH ^ 

q ^ tq 



0:! ^ 



0^ «J 



o 


'^ 


0^ 




h^ 


o 


c« 


m 




O 


Q 


hH 


1— 1 


ffl 


^ 


> 


Oh 


rt 


^ 


hH 


<l 


-«1 


1-^ 


(^ 


O 


ffi 





O 

M o 






o 

M 

H 
O 
W 

M 

Q 



O 

ft. 



in 

\- 
z 

o 

0. 



^ 



in 

t 

o 
Ph 



CO 






CO 
H 

!zi 

M 

o 



4 



CO 



;j I 



s 1 



% IS 

U 01 



N 
X 

> 

H 

a 
o 






"W5 



^ ^ 



W 



o 

Cm 
Q 









No. 30 




Sparsely settled Town, Salt Marsh, Pine Woods, Ditches, Fences, and Undefined Roads 



No. 31 




Railroads, Canals, Iron Bridges, Rocky-cliffs, Mid-river drift. Water-worn Rocks, Mixed Woods over hill curves {Harpers Ferry) 



No. 32 




^: 



1 „„^iiiiiii/fc^^^^^^ - — :^^pm:^, 






^-."l''<; 






sN^I''^ 



^%. % 



■'^: ^; 






^ 



"-.'■':. #""1 #!'% '""'' i""', '""" 



'-//'(liLs- £ 



Eroded drift banks, with boulders set free ; ajid scrub deciduous woods {Gay Head) 



No. 33 




Blocking of Cities, Large Buildings, Suburban Villas and Grounds, Fresh Marsh 



No. 34 




Erosion of Soft Stratified Rock a.ru) Gulch {Santa Cruz, California) 



NO. 35. 



Hill Cui'ves for every 20 feet difference of level. Scale 10,000" 




Slope. 


Proportion 

of 
Height to Base 


Length of Base 

I foot "of Height 

( in feet ) 


Length of Base 
20 feet of Height 

( in feet.) 


Length of Base 

20 feet'Sf Height 

( in meters ) 


1° 


1 to 57 


57. 29 


1145 . 8 


349.1 


2° 


1 to 29 


28 .64 


572.8 


174. 5 


3° 


1 to 19 


19 . 08 


381.6 


116. 3 


4° 


1 to 14 


14. 30 


286.0 


87.1 


5° 


1 to 11 


11.43 


228.6 


69.7 


10° 


1 to 6 


5 .67 


113 .4 


34.6 


15° 


1 to 4 


3. 73 


7^.6 


22. 7 


20° 


1 to 3 


2 . 75 


55.0 


16.7 


25° 


1 to 2 


2 . 14 


42.8 


13.1 


30° 


1 to 1.7 


1 .73 


34.6 


10. 5 


35° 


1 to 1.4 


1 .43 


28.6 


8. 7 


40° 


1 to 1.2 


1 . 19 


23.8 


7. 2 


45° 


1 to 1 


1 .00 


20.0 


6.1 


50° 


1 to 0.8 


0.84 


16.8 


5.1 


55° 


1 to 0.7 


0. 70 


14.0 


4.3 


60° 


1 to 0.6 


0. 58 


11.6 


3.6 



X vi 2 



A 



< 



< 

O 
CO 

>- 

UJ 

> 

CO 

d 

Q 

< 

d 
d 






U3 



-4- 



CO 






LO 



in 







< o 



O - -I 



NO. 37. 




DISTANCES IN METERS 



^ 



LRB D '1h 



